SY FOR
f(x)= x³ - 8x² + kx-20
When f(x) is divided by (x - 1), the remainder is R.
When f(x) is divided by (x - 2), the remainder is 4R.
Find the value of k.

To isolate a certain variable in an equation, we must perform inverse operations on both sides of the equal sign to cancel out values.

[tex]S=-qtr[/tex]

⇒ Right now, r is being multiplied by q and t. Divide both sides by qt to cancel these values out:

[tex]\dfrac{S}{qt}=\dfrac{-qtr}{qt}\\\\\dfrac{S}{qt}=-r[/tex]

⇒ Now, to remove the negative symbol, multiply both sides by -1:

[tex]r=-\dfrac{S}{qt}[/tex]

[tex]r=-\dfrac{S}{qt}[/tex]

Answer:

mean 33.214

Step-by-step explanation:

465/14= 33.214

Answer:

Step-by-step explanation:

(5). ( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )  

y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] )

~~~~~~~~~~~~~~~~~

( 4 , 8 )

y = [tex]\frac{1}{7}[/tex] x - 5 ; slope m = [tex]\frac{1}{7}[/tex]

Slope of line ⊥ to the given line is opposite reciprocal to [tex]\frac{1}{7}[/tex] and equal to ( - 7)

y - 8 = - 7( x - 4 )

(6).  

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )

m = [tex]\frac{ y_{2} -y_{1} }{ x_{2} -x_{1} }[/tex]

y = mx + b

~~~~~~~~~~~~

( 4 , 3 )

( 5 , 1 )

m = [tex]\frac{1-3}{5-4}[/tex] = - 2

y - 3 = - 2( x - 4 )

y = - 2x + 11

(7). y = - [tex]\frac{1}{2}[/tex] x + 2

The required given Co-ordinates are plotted in graph below.

The numbers on a direction lattice are utilized to find focuses. Each point can be recognized by an arranged sets of numbers; that is, a number on the x-axis  called a x-coordinate, and a number on the y-hub called a y-coordinate. Requested matches are written in enclosures (x-coordinate, y-coordinate).

Graph is characterized as to make an outline that shows a connection between at least two things. An illustration of diagram is to make a progression of bars on charting paper

coordinates plane so that the x-axis extends from -9 to 9 and the y-axis

extends from -6 to 6

Plotted points on the graph are shown in image below.

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Answer:

d=189 when c=4725

Step-by-step explanation:

c:d

125:5

divide by 5 to find the value of c when d=1

25:1

multiply by 6 to find the value of c when d=6

150:6

4725:?

4725/25=189

189*1=189

If you got a score of 90 percent on the test and the test is worth 20 percent of your overall grade, you would multiply 90 by 0.2 for a value of 18 points out of the possible 20 points.

Is 70 percent a failing grade?

The standard range for grades is 55 to 100. As seen in the chart below, number grades correspond to letter grades. The required passing score is 70. (C). Failure grades are any grades between 55 and 69 (D and F), for which no unit credit is granted.

A Passed grade requires a C or higher; a C- or worse results in a Not Passed mark. Many prerequisites (such as those for General Education and Electives) may be satisfied by a grade of C-, but neither credit nor requirements will be satisfied by a grade of Not Passed.

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All objects fall at the same rate in a vacuum as long as the only force acting on them is gravity.

Hence, the height of the ledge from the ground is 1.25m.

3.27m/s

Given parameters:

Initial velocity  = 3.27m/s

Height of fall  = 2.8m

Unknown:

Final velocity  = ?

To solve this problem, we have to look at our given parameters and compare to the appropriate motion equation.

we have been given;   u (initial velocity) and height of fall (h)

Since this body falls under acceleration due to gravity, g = 9.8m/s²

Now, we use;

V²  = U² + 2gh\

where V is the final velocity

Input the parameters and solve;

V² = 3.27m/s + (2 x 9.8 x 2.8)

V = 65.4m/s

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yes 38/53 is the simplest form

Step-by-step explanation:

The fraction is already reduced.

Answer:

see explanation

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

(a)

given the equation of L1 is

2x - y = 3 ( subtract 2x from both sides )

- y = - 2x + 3 ( multiply through by - 1 )

y = 2x - 3 ← in slope- intercept form

with slope m = 2

• Parallel lines have equal slopes

then slope of L2 is m = 2

given the equation of L2 is

kx + 2y = 3 ( subtract kx from both sides )

2y = - kx + 3 ( divide through by 2 )

y = - [tex]\frac{k}{2}[/tex] + [tex]\frac{3}{2}[/tex] ← in slope- intercept form

with slope m = - [tex]\frac{k}{2}[/tex]

since slope of L1 and L2 are equal, both 2 , then

- [tex]\frac{k}{2}[/tex] = 2 ( multiply both sides by 2 to clear the fraction )

- k = 4 ( multiply both sides by - 1 )

k = - 4

----------------------------------------------

(b)

given the slope of a line is m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex]

Then

for L2 to be perpendicular to L1

- [tex]\frac{k}{2}[/tex] = - [tex]\frac{1}{2}[/tex] ( multiply both sides by - 1 )

[tex]\frac{k}{2}[/tex] = [tex]\frac{1}{2}[/tex] , thus

k = 1

A linear pair's total angles are always equal to 180°. Hence ∠ HJL is 94°

given

∠HJL and  ∠LJK are linear pair

∠ HJL = ?

∠HJL +  ∠JLK =180

x + x -8 = 180

2x -8 =180

x = 188/ 2 = 94°

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Answer:

0.00000797

Step-by-step explanation:

Therefore, the solution of this problem is the domain would be

0 < t ≤ 1.61.

A function's domain is the set of possible values that can be entered. This set reflects the values of x in a function like f. (x). Its range refers to the set of possible values that a function can accept. These are the values that are returned by the function when we enter an x value.

Here,

The remaining distance that would result from multiplying the speed by the time t will be added to the 20 miles that make up the total distance. The formula for the equation would be as follows:

120 = 15 + 65t

It would be 0 hours at the very least. When the entire 120-mile distance has been accomplished, the time limit is reached.

t ≤ (120 - 15)/65

t ≤ 1.61 hours

Therefore, the solution is the domain would be 0 < t ≤ 1.61.

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Answer: Slope of [tex](-3, -2)[/tex] and [tex](-1, -5)[/tex] is [tex]-1.5[/tex].

Step-by-step explanation:

The slope of a line is given by, [tex]m=\frac{y_2-y_1{} }{x_2-x_1}[/tex]

Here we have,

[tex](x_{1}, y_{1}) = (-3, -2)[/tex] and [tex](x_{2}, y_{2}) = (-1, -5)[/tex]

Now put the known values in the slope formula we get,

[tex]m=\frac{(-5) -(-2) {} }{(-1) -(-3)}[/tex]

   [tex]m=\frac{(-3) {} }{2}[/tex]

Slope (m) = 1.5

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The data posted at the conclusion of the answer provides the finished table with the average walking rates.

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.

Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.

Imagine that your square is made up of smaller unit squares.

The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.

To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured

According to our question-

The velocity in this problem is the average walking speed, hence the distances in the table are calculated by dividing the time in the same row by the velocity.

The velocity is reported as follows for the first row:

2.5 miles per hour is equal to v = 0.5/(12/60) = 0.5/0.2.

The minutes are split by 60 because the time is in hours.

The velocity is stated as follows for the second row:

1.5 x 4/3 divided by 45/60 equals 2 miles per hour, or v.

The velocity is given as follows for the third row:

v = 0.75 x 4 x (15/60) = 4 miles per hour.

Hence, 4 miles per hour.

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Answer:

Step-by-step explanation:

0.69

The equation for this problem will be 12x = 48.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Sergio has p works of art in his craft assortment. He and other nearby canvas gatherers consented to give a sum of 48 compositions to the neighborhood historical center. Every one of the 12 authorities will give a similar number of artistic creations.

Let 'x' be the number of donations by each. The equation for this problem is given as,

12x = p

12x = 48

The equation for this problem will be 12x = 48.

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The next day Patsy have t choose between cheerleading and play practice is 17th September

To solve the problem of calculating the next day Patsy will have the events of cheerleading and school play same day, we find the lowest common multiple of the intervals of the occurrence of the two events

The interval of the events are:

cheerleading - 4th day

school play - 6th day

The Lowest common multiple of 4 and 6 is calculated to be 12

If the two events occurred on 5th September the next will on

= 5 + 12

= 17

The next time to choose between the two will be on 17th September

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Answer:

Step-by-step explanation:

Answer:

[tex]\frac{16}{6561}[/tex]

Step-by-step explanation:

[tex]\frac{2x2x2x2}{9x9x9x9}[/tex] = [tex]\frac{16}{6561}[/tex]

On #9:

Slope-intercept form is y = mx + b

Based on the graph, the slope is -4/3 and the y-intercept is (0,0).

The answer is y = –4/3 x.

You could add "+0" at the end to have y = –4/3 x +0, but since adding 0 doesn't change it, it's usually left off.

Answer:

y = -4/3x + 0 or just y = -4/3

Step-by-step explanation:

you just find the slope by doing rise over run, and find the y-intercept by looking at what number the line hits on the y-axis.

The slope of the line that connects (10,4) and (5,13) is -9/5.

Here given,

The two points are (10,4) and (5,13).

We have to find the slope that passes through the given points,

The formula to find slope(m) is,

The slope of the line that passes through (x1 , y1) and (x2,y2) is,

Slope(m) = y2 - y1 / x2 - x1

By substituting the values in x and y

Slope = 13 - 4 / 5 - 10

          = 9 / -5

Slope = -9/5

          = -1.8

Therefore the slope of line that passes through (10,4) and (5,13) is -9/5.

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Answer:

she should just divide the dimensions by 3

Step-by-step explanation:

The triangles are similar by Angle-Angle similarity since they are congruent.

According to the Angle-Angle Similarity Theorem, if two angles in one triangle are equal to two angles in another triangle, the triangles are similar. The triangles are similar if two pairs of corresponding angles in a pair of triangles are congruent. We know this because if two angle pairs are equal, then the third pair must be equal as well.

Two triangles with two angles, starting with Triangle 1, one measuring 47 degrees and the other measuring 53 degrees, are congruent to two angles in Triangle 2. Following the AA similarity theorem, it is assumed that Triangle 1 is similar to Triangle 2.

In this case, angle MNP = angle QPL (corresponding angles, //lines) (A)

angle QLP is common angle (A)

By AA, the 2 triangles are similar.

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Answer: the number is 4

Step-by-step explanation:

5x+5=25 is the equation

solve for x by isolating x

5x+5-5=25-5

5x=20

divide both sides by 5 to isolate x

x=4

Answer: 4

Step-by-step explanation:

5x + 5 = 25 this is what the equation is!

Then we subtract 5 on both side

5x = 20

Then divided by 5 on both side

x= 4

1) The dimension of the base of the pool is; (x + 3) and (x + 8)

2) The volume of the pool when x = 3 ft is;  198 ft³

3) If the volume is 100 ft³ of water, the height x is; 2 ft

4) If the maximum capacity of the pool is 520 ft³, the maximum depth is; 5 ft

We are given that the volume of water in a rectangular, in-ground, swimming pool is; V(x) = x³ + 11x² + 24x

where;

V(x) is the volume in cubic feet when the water is x ft high

1) V(x ) =x³ + 11x³ + 24x

V(x) is the volume in cubic feet when the water is x ft high

Factorizing the polynomial into its' factors gives;

V(x) = x(x² + 11x + 24)

V(x) = x(x + 8)(x + 3)

The water is x ft high and so the dimensions of the base of the pool are (x + 3) and (x + 8)

2) We want to find the volume of the pool when x = 3 ft. Thus;

V(3) = 3(3 + 8)(3 + 3)

V(3) = 3 (11)(6)

V(3) = 198 ft³

3) If the volume is 100 ft³ of water, the height x is calculated as;

x(x + 8)(x + 3) = 100

Solving for x gives us;

x = 2 ft

4) If maximum capacity of the pool is 520 ft³, then the maximum depth is;

x(x + 8)(x + 3) = 520

Solving for x gives us;

x = 5 ft

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The measure of the acute angles in the right triangle are 10 and 80 degrees.

A right angle triangle is a triangle that has one of its angles as 90 degrees.  The sides of a right angle triangle can be named base on the position of the angles. The sides includes hypotenuse side, opposite side and adjacent side.

The sum of angles in a right angle triangle is 180 degrees.  

The other measures of the right triangle are acute angles.

Any angle that measures greater than 0° and less than 90° is called an acute angle.

Hence, let's find the measure of the acute angles

let

x = measure of one acute angle

Hence,

x + 8x + 90 = 180

9x = 180 - 90

9x = 90

x = 90 / 9

x = 10

Therefore, the measure of the acute angles are 10 and 80 degrees.

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The rate of width changing will be;

⇒ 4 feet/hour

What is mean by Rectangle?

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The length of a rectangular drainage pond is changing at a rate of 8 ft/hr and the perimeter of the pond is changing at a rate of 24 ft/hr.

Now,

We know that;

⇒ Perimeter of rectangle = 2 (Length + Width)

Substitute al the values, we get;

⇒ 24 = 2 (8 + x)

⇒ 12 = 8 + x

⇒ x = 12 - 8

⇒ x = 4

Thus, The rate of width changing will be;

⇒ 4 feet/hour

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Answer:

divide 2x by 2, that gives you x, then divide 104 by 2 and that gives you the answer to x