Help me please I need it.

y = x - 4 is  the equation of the line in slope-intercept form.

How do you interpret a slope-intercept form?

The data provided by that form can be used to graph a linear equation in slope-intercept form. As an illustration, the equation y=2x+3 indicates that the line's slope is 2 and that its y-intercept is located at (0,3). This reveals the single point at which the line passes as well as the direction in which we should draw the full line after that.

Point from graph = (2, -2 )

                slope (m) = y/x

                                = -2/2

                                = 1

slope-intercept form ⇒ y = mx + c    

                                        -2 = 1 * 2 + c

                                          - 2 = 2 + c

                                               c = -4

 slope-intercept form ⇒ y = x - 4

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Answer:

C. The items have different y-intercepts and different rates of change

Step-by-step explanation:

Figure I shows a linear equation in the form y = mx + b, where "m" is the rate of change and "b" is the y-intercept. That means for y = 1/4 * x - 1/2, 1/4 is the slope and 1/2 is the y-intercept.

Figure II shows a table. The y-intercept is when x = 0, so look at where x = 0 is in the table and see the y-value which corresponds to it. The y-value in this case would be -0.25. To find the rate of change, assuming Table II is changing at a constant rate, subtract the subsequent y-value from a proceeding y-value and divide that by subtracting the corresponding x-values (any two sets of x and y-values should work): (3.75 - 7.75)/(-1 - -2) = -4/(-1 + 2) = -4/-1 = 4.

Thus, we know that the rates of change are different and the y-intercepts are different for both functions.

Step-by-step explanation:

All you have to do is to multiply the length times width times height to get the area. So its 6 x 20 x q1/4 ft = 30q. Hope this helps.

Answer:

B. 6

Step-by-step explanation:

A is between P and R

Correct option is B. 6

Therefore, all values of x that are less than or equal to -3 make up the inequality's solution set.

An inequality in mathematics is a claim that two values or expressions are not equivalent to one another. A relationship between two values, where one value is larger than, less than, or not equal to the other, is expressed by an inequality. The inequality marks "" (less than), ">" (greater than), "=" (less than or equal to), ">=" (greater than or equal to), and "" can be used to denote an inequality (not equal to).

given

The disparity is as follows:

-3x + 2 ≥ 11

By subtracting 2 from both sides of the inequality and then dividing the result by -3, we can separate x on one side of the inequality .

-3x + 2 - 2 ≥ 11 - 2

-3x ≥ 9

x ≤ -3

Therefore, all values of x that are less than or equal to -3 make up the inequality's solution set.

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Answer:

H₀: μ = 550 vs. Hₐ: μ < 550.

Step-by-step explanation:

A researcher believes that the mean scores for this year's college seniors in the Philippines who are interested in pursuing graduate management education will be less than 550.

The mean sore for all test‑takers is μ = 550 with a standard deviation of σ = 120.

A random sample of n = 250 college seniors in the Philippines interested in pursuing graduate management education who plan to take the GMAT were selected.

The null and alternative hypotheses for the study of the performance on the GMAT of college seniors in the Philippines is as follows:

H₀: The mean scores for this year's college seniors in the Philippines who are interested in pursuing graduate management education will not be less than 550, i.e. μ = 550.

Hₐ: The mean scores for this year's college seniors in the Philippines who are interested in pursuing graduate management education will be less than 550, i.e. μ < 550.

Answer:

\(\frac{1}{2-tan(y)} = \frac{3\sqrt{3}}{6\sqrt{3}-1}\)

After Rationalising:

\(\frac{1}{2-tan(y)} = \frac{54 +3\sqrt{3}}{107}\)

Step-by-step explanation:

tan(x) = 3√3

x + y = 90 (complimentary angles)

⇒ x = 90 - y

tan(\(\frac{\pi}{2}\) - θ) = cot(θ)

⇒ tan(90 - θ) = cot(θ)

⇒ tan(90 - y) = cot(y)

⇒ tan(x) = cot(y)

⇒ cot(y) = 3√3

⇒ \(\frac{1}{tan(y)}\) = 3√3

⇒ tan(y) = \(\frac{1}{3\sqrt{3}}\)

\(2-tan(y) = 2 - \frac{1}{3\sqrt{3}} \\\\= \frac{2*3\sqrt{3} -1}{3\sqrt{3} } \\\\= \frac{6\sqrt{3} -1}{3\sqrt{3} }\\\\\\\implies \frac{1}{2-tan(y)} \\\\= \frac{3\sqrt{3}}{6\sqrt{3}-1}\)

Multiply and divide by : 6(√3) + 1

\(\frac{3\sqrt{3}}{6\sqrt{3}-1}\frac{6\sqrt{3}+1}{6\sqrt{3}+1}\\ \\= \frac{(3*6*\sqrt{3}*\sqrt{3}) + 3\sqrt{3}}{6^2 * (\sqrt{3})^2 -1^2}\\\\= \frac{18*3 +3\sqrt{3}}{36*3 -1}\\\\= \frac{54 +3\sqrt{3}}{108-1}\\\\= \frac{54 +3\sqrt{3}}{107}\)

Answer:

Step-by-step explanation:

The given relations let us write three equations in the unknown quantities.

Let x, y, z represent the amounts received by the first, second, and third person, respectively. Then the problem statement tells us ...

  x + y + z = 127 . . . . . . $127 was divided

  2x - y = 5 . . . . . . . . second got $5 less than twice the first

  -y +z = 2 . . . . . . . third got $2 more than the second

Subtracting the second equation from twice the first gives ...

  2(x +y +z) -(2x -y) = 2(127) -(5)

  3y +2z = 249 . . . . . . . simplify (x is eliminated)

Subtracting twice the third equation gives ...

  (3y +2z) -2(-y +z) = (249) -2(2)

  5y = 245 . . . . . . . . simplify (z is eliminated)

  y = 49 . . . . . . . . . divide by 5

  z = 2+y = 51 . . . . find z

  x = 127 -(49 +51) = 27 . . . . find x

The first received $27; the second received $49; and the third received $51.

Answer:

let the 1st received be x

let the 2nd received be 2x-5

let the 3rd received be 2x-5t+2= 2x+3

Total=127

x+2x-5+2x-3=127

5x=135.

x=27 is for the 1st person

2x-5=2×27-5=49 is for the 2nd person

2x-5=2×27-3=51.

The correct two - way frequency table for the data on High School Students, and the kind of band they want to play at the school dance, is:

                                                     Rap          Rock           Country      Total

Grades 9 - 10                                40              30                55              125

Grades 11 - 12                                60              25                35              120

Total                                              100              55                90             245

Option A is therefore correct.

In a two-way frequency table, there will be totals for both the rows and the columns.

The totals for the rows in this instance are:

Grade 9 - 10 totals :

= 40 + 30 + 55

= 125

Grade 11 - 12 :

= 60 + 25 + 35

= 120

The totals for the columns are:

Rap totals :

= 40 + 60

= 100

Rock :

= 30 + 25

= 55

Country :
= 55 + 35

= 90

Two-way frequency tables allow for us to be able to conclude on the event described by looking at totals from both the columns and the rows. This gives a clearly understanding on preferences and categories.

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The value of t₄ in the arithmetic sequence is 103/8.To determine the value of t₄ in an arithmetic sequence, we need to use the given information that t₁ = 11 (the first term of the sequence) and S₉ = 243 (the sum of the first 9 terms of the sequence).

We know that the formula for the sum of an arithmetic sequence is Sₙ = (n/2)(2a + (n-1)d), where Sₙ is the sum, a is the first term, n is the number of terms, and d is the common difference.

From the given information, we have S₉ = 243, a = 11, and n = 9. Plugging these values into the sum formula, we can solve for d:

243 = (9/2)(2(11) + (9-1)d)

243 = 9(22 + 8d)

243 = 198 + 72d

45 = 72d

d = 45/72 = 5/8

Now that we have the common difference, we can find t₄ using the formula for the nth term of an arithmetic sequence:

tₙ = a + (n-1)d

t₄ = 11 + (4-1)(5/8)

t₄ = 11 + 3(5/8)

t₄ = 11 + 15/8

t₄ = 88/8 + 15/8

t₄ = 103/8

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Note that in the prompt above, the value of x is given as: 16°

To answer the issue, we will first name all of the points supplied to us on the isosceles triangle, then identify O, and last discover the value of x. See the attached image.

As a result, an isosceles triangle has two equal sides and two equal angles. The term is derived from the Greek words iso (same) and skelos (skull) (leg). An equilateral triangle has all of its sides equal, whereas a scalene triangle has none of its sides equal.

In ΔAOB

OA =  OB = R, the radius of the circle O,

therefore, the ΔAOB is an isosceles triangle, with OA, OB as the congruent sides and AB as the base of the triangle.

Thus, ∠OAB = ∠OBA = 53°

Sum of all the angles of a triangle = 180°

∠O + ∠AOB + ∠OBA = 180°

We know ∠AOB = ∠OBA, therefore,

∠O + 2(∠AOB) = 180°

∠O + 2(53°) = 180°
∠O = 180 - 106

∠O = 74°

In ΔOBC,

BC is the tangent to the circle O, therefore,

∠OBC = 90°

Sum of all the angles of a triangle = 180°

∠O + ∠OBC + ∠OCB = 180°

74° + 90° + ∠OCB = 180°

∠OCB = 180° - 74° - 90°

∠OCB = 16°

Hence, the value of x is 16°.

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Then, multiply this result by 100 to get the percentage. In this case, 120 is 80% of 150.

To use a double number line diagram to find what percent 120 is of 150, you need to create a diagram with two parallel lines. On the top line, mark 150 at one end and 100 at the other.

On the bottom line, mark 120 at one end and leave the other end blank. Then, draw diagonal lines connecting 120 on the bottom line to 150 on the top line and 100 on the top line to the blank end of the bottom line.

This creates two triangles. The height of the triangle with 120 is the percentage you're looking for.

To find this percentage, divide the length of the diagonal line connecting 120 and 150 by the length of the diagonal line connecting 100 and the blank end of the bottom line.

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Answer:

The answer is that image below. If it isn't correct, I'm sorry.

Answer:

1,800

Step-by-step explanation:

divide 1,000 by 6.25 and we get

160 then we multiply 160 by 5 and we

get 800 so Bill's Bill's bank account will be worth

1,800 in 5 years

Answer:

Thanks

Step-by-step explanation:

Thanks

Answer:

121

Step-by-step explanation:

Find out the amount of units Ismail have more than Johan.

11 - 7 = 4 units

Since Ismail has 44 more sweets than Johan and 4 more units..

4 units = 44

1 units = 44 ÷ 4 = 11

Altogether, there's 11 units.

11 units = 11 x 11 = 121

Answer:

x = 23.6°

Step-by-step explanation:

The given diagram shows a right triangle with an unknown angle, x.

We have been given the measures of the hypotenuse of the triangle and the measure of the side opposite unknown angle. Therefore, we can use the sine trigonometric ratio to find the value of x.

\(\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

The unknown angle is x, so θ = x.

The side opposite the angle measures 6 units, so O = 6.

The hypotenuse of the triangle measures 15 units, so H = 15.

Substitute the values into the ratio and solve for x:

\(\sin x=\dfrac{6}{15}\)

     \(x=\sin^{-1}\left(\dfrac{6}{15}\right)\)

     \(x=23.5781784...\)

     \(x=23.6^{\circ}\; \sf (nearest\;tenth)\)

Therefore, the value of x is 23.6°.

The appropriate equation to solve for the missing angle is sin(x) = 6/15

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

The right triangle

From the triangle, we have

Angle x

Also, we have the following sides in relation to x

Opposite = 6

Hypotenuse = 15

This means that we make use of the sine ratio

i.e. sin = opposite/hypotenuse

Using the above as a guide, we have the following:

sin(x) = 6/15

Hence, the equation is sin(x) = 6/15

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Answer:

1-2 ft apart because the radius angle would be 2ft since its not a straight forward lining its horizontal.

Step-by-step explanation:

There must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

To prove the existence of a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can employ a contradiction argument. Assume that such a vertex u does not exist.

Since the number of vertices in T is odd, there must be at least one path from v to another vertex w such that the distance between v and w is greater than (n-1)/2.

Denote this path as P. Let x be the vertex on path P that is closest to v.

By assumption, the distance from x to v is greater than (n-1)/2. However, the remaining vertices on path P, excluding x, must have distances at least (n+1)/2 from v.

Therefore, the total number of vertices in T would be at least n + (n+1)/2 > n, which is a contradiction.

Hence, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

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Question:

A number cube with faces labeled from 1 to 6 will be rolled once.  The number rolled will be recorded as the outcome.

Give the sample space describing all possible outcomes.  Then give all of the outcomes for the event of rolling a number greater than 2.

If there is more than one element in the set, separate them with commas.

Answer:

\(S = \{1,2,3,4,5,6\}\)

\(Greater2 = \{3,4,5,6\}\)

Step-by-step explanation:

Given

A roll of a 6 sided number cube

Solving (a): The sample space

This implies that we list out all number on the number cube.

So:

\(S = \{1,2,3,4,5,6\}\)

Solving (b): Outcomes greater than 2

This implies that we list out all number on the number cube greater than 2 i.e. 3 to 6.

So:

\(Greater2 = \{3,4,5,6\}\)

\( = 4 - 4 \: log_{5}(10) - 4 log_{2}(10) + 4 log_{2}(10) log_{5}(10) \\ \\ or \: \\ \\ = 4\)

the answer is 2

see the attachment for explanation

Answer:

Answer is 2). 4

Explanation:

\({ \rm{(2 - log_{ \sqrt{2} }10)(2 - log_{ \sqrt{5} }10)}}\)

• let's open the brackets:

\({ \rm{(2 \times 2) + (2 \times - log_{ \sqrt{5} }10 ) + (2 \times - log_{ \sqrt{2} }10) + ( log_{ \sqrt{2} }10 \times log_{ \sqrt{5} }10) }} \\ \\ = { \rm{4 - 2 log_{ \sqrt{5} }10 - 2 log_{ \sqrt{2} }10 + ( log_{ \sqrt{5} }10)( log_{ \sqrt{2} }10)}}\)

• change log√5 to log√2:

\({ \rm{4 - 2 log_{ \sqrt{2} }10 - (\frac{2 log_{ \sqrt{2} }10 }{ log_{ \sqrt{2} } \sqrt{5} } ) + ( log_{ \sqrt{2} }10)( \frac{ log_{ \sqrt{2} }10 }{ log_{ \sqrt{2} } \sqrt{5} } )}} \\ \\ = { \rm{4 - 2 log_{ \sqrt{2} }10 - ( \frac{4 log_{ \sqrt{2} }10}{ log_{ \sqrt{2} } \sqrt{5} }) }} \\ \\ = { \rm{4 - 2 log_{ \sqrt{2} }10 - ( \frac{8 log_{ \sqrt{2} }(5 \times 2) }{ log_{ \sqrt{2} }5} )}} \\ \\ = { \rm{4 - 2 log_{ \sqrt{2} }(5 \times 2) - \frac{8 log_{ \sqrt{2} }2}{ log_{ \sqrt{2} }5 } }} \)

• now let's change log√2 to log10

\( = { \rm{4 - \frac{2 log_{10}10}{ log_{10} \sqrt{2} } - \frac{8 log_{10}2}{ log_{10} \sqrt{2} } \div \frac{ log_{10}5 }{ log_{10} \sqrt{2} } }} \\ \\ = { \rm{4 - \frac{2}{0.3} - \frac{2.41}{0.3} \times \frac{0.3}{0.7} }} \\ \\ = { \rm{4 + \frac{41}{70} }} \\ \\ { \rm{ = 4 \frac{41}{70} \: \approx \: 4 }}\)

Answer:Go from -4 1 up one to the side

Step-by-step explanation:on the y axis you must go to negative four then continue in a one by one straight line.

The answer is 1) V = \(2\pi\int\limits(2)+ {x} \, dx\); 2) V = \(2\pi \int\limits(1 - 2x) - 2x dx\); 3) V =\(2\pi \int\limits {\sqrt{2} } \, dx\) ; 4) V = \(2\pi\int\limits {\sqrt{(-2/2)(2-2)} \ dx\) .

1) The volume of the shell is then given by the product of the area of its curved surface and its height. The height is equal to 2 - (-2) = 4, and the radius is equal to the minimum of the distances from x = 2 to the two curves, which is x = 2 - () = 2 + . The volume of the solid is then given by the definite integral:

V = \(2\pi\int\limits(2)+ {x} \, dx\) = \(2\pi [(/3) + 2x]\) evaluated from 0 to 1 = (4/3)π.

2) The height of the region is equal to  - (2x) =  -2x, and the radius is equal to the minimum of the distances from x = 1 to the two curves, which is x = 1 - (2x) = 1 - 2x. The volume of the solid is then given by:

V = \(2\pi \int\limits(1 - 2x) - 2x dx\)=\(2\pi [/5 - 2/3 + /2]\) evaluated from 0 to 1 = (8π/15).

3) The height of the region is equal to (2-x) -  = 2-x. The radius is equal to the minimum of the distances from x = 0 to the two curves, which is x = The volume of the solid is then given by:

V =\(2\pi \int\limits {\sqrt{2} } \, dx\) = \(2\pi [(x^4/4)]\) evaluated from 0 to √2 = (π/2).

4) The height of the region is equal to () - (2-) = 2 - 2. The radius is equal to the minimum of the distances from x = 0 to the two curves, which is x = √((2-)/2). The volume of the solid is then given by:

V = \(2\pi\int\limits {\sqrt{(-2/2)(2-2)} \ dx\) = \(4\pi [(2/3)\± (2\sqrt{2} /3)]\)

The complete Question is:

Use the shell method to find the volumes of the solids generated by revolving the regions bounded by the curves and lines in about the

1.  y = x, y = -x/2, and x = 2

2. y = 2x, y = x/2, and x = 1

3. y = x/2, y = 2-x, and x = 0

4. y = 2-x/2, y = x/2, and x = 0

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Answer:

y= 2x -6

Step-by-step explanation:

The slope-intercept form of a line is given by y= mx +c, where m is the slope and c is the y-intercept.

To find the equation of a line, two information are needed:

Given that the slope is 2, m= 2. Substitute m= 2 into y= mx +c:

y= 2x +c

Let's find the coordinate in which the line intersects the line 2x -3y= 6. Point of intersection refers to the point at which two lines cuts through each other i.e., the point lies on the graph 2x -3y= 6 and the line of interest.

2x -3y= 6

When x= 3,

2(3) -3y= 6

6- 3y= 6

3y= 6 -6

3y= 0

Divide both sides by 3:

y= 0

Coordinate that lies on the graph is (3, 0).

Substitute the point into the equation and solve for c:

y= 2x +c

When x= 3, y= 0,

0= 2(3) +c

0= 6 +c

c= -6

Substitute the value of c back into the equation:

Thus, the equation of the line in slope-intercept form is y= 2x -6.

Additional:

For a similar question on slope-intercept form, do check out the following!

Answer:

$0.64 per cup

Step-by-step explanation:

There are 16 cups in 1 gallon, so the number of cups in 2 gallons is:

1 gallon: 16 cups

2 gallon = 2 x 1 gallon = 2 x 16 cups = 32 cups

So we need to find the price of each cup:

1 cup = ($20.48 / 32 cups) = $0.64 per cup.

Each function on the left should be matched to all points on the right that would be located on the graph of the function as follows;

f(x) = 2x + 2         ⇒   (0, 2).

f(x) = 2x² - 2        ⇒   (-1, 0).

\(f(x) = 2\sqrt{x+1}\)   ⇒   (0, 2).

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.

Next, we would determine the point or ordered pair that represent a solution on the graph of each of the function as follows;

For the ordered pair (0, 2), we have:

f(x) = 2x + 2

2 = 2(0) + 2

2 = 2 (True).

For the ordered pair (-1, 0), we have:

f(x) = 2x² - 2

0 = 2(-1)² - 2

0 = 2 - 2

0 = 0 (True).

For the ordered pair (0, 2), we have:

\(f(x) = 2\sqrt{x+1}\\\\2= 2\sqrt{0+1}\\\\2 = 2\sqrt{1}\)

2 = 2 (True).

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The equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.

To calculate the equivalent ratio of 1.25 : 3.75 : 7.5, we need to find a common multiplier that can be applied to all the numbers in the ratio to make them whole numbers. In this case, the common multiplier is 4 because it can be multiplied to each number to eliminate the decimals.

By multiplying each number in the ratio by 4, we get:

1.25 * 4 = 5

3.75 * 4 = 15

7.5 * 4 = 30

So the equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.

This means that the relative sizes or quantities represented by the original ratio are maintained in the equivalent ratio. For example, if we had 1.25 units of something, it would be equivalent to 5 units in the new ratio, and if we had 7.5 units, it would be equivalent to 30 units in the new ratio.

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Answer:

2 and 4

Step-by-step explanation:

1)

14x+6=2(5x+3)

14x+6=10x+6

No Solutions

2)

3(x-5)+6=x-(9-2x)

3x-9=3x-9

Infinitely Many

3)

2+5x-9=3x+2(x-7)

5x-7=5x-14

No Solutions

4)

3(4x-6)+2=-4(4-3x)

12x-16=12x-16

Infinitely Many