If PR = 4x – 2 and RS = 3x – 5, which expression represents PS?

An estimate of the mean travelling time will be 24.8 mins.

The mean is the average value which can be calculated by dividing the sum of observations by the number of observations

Mean = Sum of observations/the number of observations

Given;

Time > timemark > frequency

0 – 10 > 10/2 = 5 > 5

10 – 20 > (10+20)/2 = 15 > 15

20 – 30 > (20+30)/2 = 25 > 13

30 – 40 > (30+40)/2 = 35 > 10

40 – 50 > (40+50)/2 = 45 > 7

The mean time for the 50 people can be calculated as;

Mean = Summation of (mid-time x frequency) / total frequency

Mean = [5x5 + 15x15 + 25x13 + 35x10 + 45x7] / 50

Mean = [25 + 225 + 325 + 350 + 315] / 50

Mean = 1240 / 50

Mean = 24.8 mins

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We have the equation of a line:

[tex]y=-\dfrac{5}{4}x-1[/tex]

The formula of a slope of a line passes through points A, B:

[tex]A(x_A,\ y_A),\ B(x_B,\ y_B)\\\\m=\dfrac{y_B-y_A}{x_B-x_A}[/tex]

Complete the table:

Put the values of x to the equation of a line and calculate the value of y:

[tex]x=0\\\\y=-\dfrac{5}{4}\cdot0-1\\\\y=-1\\\\\\x=4\\\\y=-\dfrac{5}{4}\cdot4-1\\\\y=-6[/tex]

Substitute to the formula of a slope:

[tex]m=\dfrac{-6-(-1)}{4-0}\\\\m=\dfrac{-6+1}{4}\\\\\huge\boxed{m=-\dfrac{5}{4}}[/tex]

The method that can be used to write the equation of a line in slope-intercept form given two points is option A.

When a person wants to write the equation of a line in slope-intercept form given two points, he would have to:

Therefore, the answer is option A.

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Answer: y = 0.75x + 80

Step-by-step explanation:

let x = 1 mile

y = 0.75x + 80

Step-by-step explanation:

The lcm of first question is 630 and second is 840

Answer:

LCM of 15,18,21: 630

LCM of 56,84,140: 840

Step-by-step explanation:

The right method is to list all the multiples of the number and circle the least common ones. In this way you will get your answer for any LCM question!

Quadrilateral A'B'C'D' is the image of quadrilateral ABCD under a rotation about point P at; D: 105°

From the given image, If we connect points C of the blue quadrilateral to point C' of the rotated quadrilateral using the center of rotation P, then we will notice that ∠CPC' will be greater than 90°.

Now, the rotation is counterclockwise and it therefore means that the angle of rotation is will be positive and since ∠CPC' is greater than 90°, then we can say that the only correct option is Option D which is 105°

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Answer:

C

Step-by-step explanation:

calculate the slope m using the slope formula

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

with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (4, 0) ← 2 points on the line

m = [tex]\frac{0-2}{4-0}[/tex] = [tex]\frac{-2}{4}[/tex] = - [tex]\frac{1}{2}[/tex]

the y- intercept is the value of y where the line crosses the y- axis , then

y- intercept = 2

Option 1 corresponds to Part B , Option 2 corresponds to Part D , Option 3 corresponds to Part A , Option 4 corresponds to Part C

The complete question is attached in the image

An expression corresponds to the mathematical statement that consists of variables , Constants and mathematical operators  simultaneously.

Solving the given option will give us the answer.

(x²+15x+65)+(2x-5)*(3x+8)

(x²+15x+65)+(6x²+16x-15x-40)

(7x²+16x+25)

Option 1 corresponds to Part B

(4x+1)*(3x-4)-(5x²-10x-12)

(4x+1)*(3x-4)-(5x²-10x-12)

(12x²-16x+3x-4)-(5x²-10x-12)

(7x²-3x+8)

Option 2 corresponds to Part D

(8x²+19x+4)+(3x+2)*(x-5)

(8x²+19x+4)+(3x²-15x+2x-10)

(11x²+6x-6)

Option 3 corresponds to Part A

(6x+1)*(3x-7)-(7x²-34x-20)

(18x²-42x+3x-7)-(7x²-34x-20)

(11x²-5x+13)

Option 4 corresponds to Part C

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A slope is also known as the gradient of a line. Slope of a line or straight object is the ratio of how much amount of rise occurs in correspondence to the increment in the run.

A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.

Slope of a line or straight object is the ratio of how much amount of rise occurs in correspondence to the increment in the run.

Thus, we get:

Slope = rise/ run

The slope of any line can found by finding the ratio of the vertical distance to horizontal distance between two ends. Therefore, the blanks can be filled as shown below.

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Answer:

[tex]a_{n}[/tex] = 100n - 78

Step-by-step explanation:

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

given a₁₄ = 1322 and a₃₈ = 3722 , then

a₁ + 13d = 1322 → (1)

a₁ + 37d = 3722 → (2)

subtract (1) from (2) term by term to eliminate a₁

24d = 2400 ( divide both sides by 24 )

d = 100

substitute d = 100 into either of the 2 equations and solve for a₁

substituting into (1)

a₁ + 13(100) = 1322

a₁ + 1300 = 1322 ( subtract 1300 from both sides )

a₁ = 22

then nth term formula is

[tex]a_{n}[/tex] = 22 + 100(n - 1) = 22 + 100n - 100 = 100n - 78

Answer:

45 degrees

Step-by-step explanation:

A bisector divides an angle into two equal parts. Since we are dividing a 90 degree angle by 2, we get a resulting value of 45 degrees.

Answer:

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

Imagine the height of the triangle is h, which is perpendicular to 15 m side.

The area is:

Use this formula and given values and find the value of h:

Since h is opposite to 30° angle and x is the hypotenuse of the formed right triangle, we'll use the property of 30°x60°x90° triangle.

In our case h is opposite to 30° angle, therefore we have:

Answer:

x = 16

Step-by-step explanation:

the area (A) of the triangle is calculated as

A = [tex]\frac{1}{2}[/tex] absinC

where a, b are 2 sides of the triangle and C the angle between them

here a = 15, b = x, C = 30° and A = 60 , then

[tex]\frac{1}{2}[/tex] × 15 × x × sin30° = 60

7.5x × [tex]\frac{1}{2}[/tex] = 60 ( multiply both sides by 2 to clear the fraction )

7.5x = 120 ( divide both sides by 7.5 )

x = 16

Answer:

888

Step-by-step explanation:

Sahil chooses a number, [We'll call it x]

divides it by 8 ,   [x/8]

adds 8 to the answer.  [(x/8) + 8]

Then multiples the answer with 8 .  [((x/8) + 8)*8]

He obtains the result as 952 .   [((x/8) + 8)*8 = 952]

The number he chooses in the beginning was

((x/8) + 8)*8 = 952

x + 64 = 952

x = 888

CHECK:

Does (888/8 + 8)*8 = 952?

(119)*8 = 952?   YES

The number is 888

Answer:

The correct option is 3.

Step-by-step explanation:

It is given a graph of an inequality with a solid line through the points (0, −2) and (2, 1) with shading above the line.

The equation of a solid line is:

[tex]y-y_{1} = \frac{y_{2}- y_{1} }{x_{2}- x_{1} } (x-x_{1})\\ y+2= \frac{1+2}{2-0}(x-0)\\ y+2= \frac{3}{2} x[/tex]

The y-intercept of the line is -2 and the shaded region is shading above the line. So, (0,0) must be lies in the shaded region.

Check the related equation by point (0,0).

0+2 =[tex]\frac{3}{2}(0)[/tex]

2 = 0

The statement is true if and only if the sign is greater than or equal instead of equal.

The required inequality is

[tex]y+2 \geq \frac{3}{2}x[/tex]

Multiply both sides by 2.

[tex]2y + 4 \geq 3x\\4\geq 3x-2y\\3x-2y \leq 4[/tex]

Therefore option 3 is correct.

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Answer:

[tex]\frac{q+p}{2(p-q)}[/tex]

Step-by-step explanation:

[tex]\frac{4(p+q)}{p-q} *\frac{q+p}{8(p+q)}[/tex]

We will cancel out like terms.

[tex]\frac{4}{p-q} *\frac{q+p}{8}\\=\frac{4(q+p)}{8(p-q)} \\=\frac{q+p}{2(p-q)}[/tex]

Answer:

14.

Step-by-step explanation:

If f(x) = 2x2 + 3x and g(x) = x - 2, (f + g)(2) is 14.

Answer:

14

Step-by-step explanation:

f(x) = 2x² + 3x

f(2) = 2 * 2^2 + 3(2) = 2*4 + 6 = 8+6 = 14

g(x)= x - 2

g(2) = 2-2 = 0

(f+ g)(2) = 14+0 = 14

1) -15+4r=-9

-15+4r=-9

We move all terms to the left:

-15+4r-(-9)=0

We add all the numbers together, and all the variables

4r-6=0

We move all terms containing r to the left, all other terms to the right

4r=6

r=6/4

r=1+1/2

2) 5-y/3=-1

5-y/3=-1

We move all terms to the left:

5-y/3-(-1)=0

We add all the numbers together, and all the variables

-y/3+6=0

We multiply all the terms by the denominator

-y+6*3=0

We add all the numbers together, and all the variables

-1y+18=0

We move all terms containing y to the left, all other terms to the right

-y=-18

y=-18/-1

y=+18

3) 42=-5x-8

42=-5x-8

We move all terms to the left:

42-(-5x-8)=0

We get rid of parentheses

5x+8+42=0

We add all the numbers together, and all the variables

5x+50=0

We move all terms containing x to the left, all other terms to the right

5x=-50

x=-50/5

x=-10

Answer:

566

Step-by-step explanation:

I got it right..................

Answer:

the answer you're looking for is 60 inches

The perimeter of the base is 4 s since it is a square.

The area of the base is s².

[tex]\boldsymbol{CST=\dfrac{1}{2}(64)(17)+256=544+256=800 \ inches^{2} }[/tex]

[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]

Answer:

[tex]\large {\textsf{B and E}}\ \implies x_1=-2\sqrt{5}-3,\ x_2=+2\sqrt{5}-3[/tex]

Step-by-step explanation:

Quadratic Formula: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Quadratic Equation: ax² + bx + x = 0, where a ≠ 0

Given equation: x² + 6x + 9 = 20

Step 1: Subtract 20 from both sides.

x² + 6x + 9 - 20 = 20 - 20

⇒ x² + 6x - 11 = 0

Step 2: Identify the values of a, b, and c and substitute them in the formula.

⇒ a = 1, b = 6, c = -11

[tex]x=\dfrac{-6\pm\sqrt{\bold{6^2}-4(1)(-11)}}{\bold{2(1)}}\\\\x=\dfrac{-6\pm\sqrt{36\bold{\ - \ 4(-11)}}}{2}\\\\x=\dfrac{-6\pm\sqrt{\bold{36+44}}}{2}\\\\x=\dfrac{-6\pm\sqrt{80}}{2}\\\\x=\dfrac{-6\pm\sqrt{16\times5}}{2}\implies \dfrac{-6\pm\sqrt{\bold{16}}\times\sqrt{5}}{2} \\\\x=\dfrac{-6\pm4\sqrt{5}}{2}[/tex]

Step 3: Separate into possible cases.

[tex]x_1=\dfrac{-6-4\sqrt{5}}{2}\implies \dfrac{-6}{2}+\dfrac{-4\sqrt{5}}{2}\implies \boxed{-3-2\sqrt{5}\ \ \textsf{or}\ -2\sqrt{5}-3}\\\\x_2=\dfrac{-6+4\sqrt{5}}{2}\implies \dfrac{-6}{2}+\dfrac{4\sqrt{5}}{2}\implies \boxed{-3+2\sqrt{5}\ \ \textsf{or}\ \ 2\sqrt{5}-3}[/tex]

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Answer:

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

As usual in trigonometry, there are so many relationships between the trigonometric functions, there is bound to be more than one method to arrive at the answer.

Knowing values for the sine and cosine function for certain angles on the unit circle proves to be quite helpful.  In general, I recommend 0°, 30°, 45°, 60°, and 90° at a minimum.

Recall the following 6 things:

Knowing these 6 things (4 things from the unit circle, a way to write the tangent function in terms of sine and cosine, and the definition of a squared trig function), we can simplify the given expression down to a single number:

The definition of the tangent squared function is that the output of the tangent function is squared...

[tex]\dfrac{1-\tan^2(30^o)}{1+\tan^2(60^o)}=\dfrac{1-(\tan(30^o))^2}{1+(\tan(60^o))^2}[/tex]

Using fact 5, and turning the tangent function into sines and cosines...

[tex]=\dfrac{1-\left(\frac{\sin(30^o)}{\cos(30^o)}\right)^2}{1+\left(\frac{\sin(60^o)}{\cos(60^o)}\right)^2}[/tex]

Using facts 1-4, and substituting known values for sines and cosines...

[tex]=\dfrac{1-\left(\frac{(\frac{1}{2})}{(\frac{\sqrt{3}}{2})}\right)^2}{1+\left(\frac{(\frac{\sqrt{3}}{2})}{(\frac{1}{2})}\right)^2}[/tex]

Division is multiplication by the reciprocal...

[tex]=\dfrac{1-\left(\frac{1}{2}*\frac{2}{\sqrt{3}}\right)^2}{1+\left(\frac{\sqrt{3}}{2}*\frac{2}{1}\right)^2}[/tex]

Reducing/simplifying common factors of 2...

[tex]=\dfrac{1-\left(\frac{1}{\sqrt{3}}\right)^2}{1+(\sqrt{3})^2}[/tex]

Squaring a square root...

[tex]=\dfrac{1-\left(\frac{1}{3}\right)}{1+(3)}[/tex]

Finding a common denominator...

[tex]=\dfrac{\frac{3}{3}-\frac{1}{3}}{4}[/tex]

Definition of subtracting fractions...

[tex]=\dfrac{\frac{3-1}{3}}{4}[/tex]

Arithmetic...

[tex]=\dfrac{\frac{2}{3}}{4}[/tex]

Division is multiplication by a reciprocal...

[tex]=\dfrac{2}{3}*\dfrac{1}{4}[/tex]

Simplification and reducing the fraction...

[tex]=\dfrac{1}{6}[/tex]

So, [tex]\dfrac{1-\tan^2(30^o)}{1+\tan^2(60^o)}=\dfrac{1}{6}[/tex]

Answer:

$42.95

Step-by-step explanation:

If Chris lost $8.59 playing poker in one week, in five weeks he would lose $42.95.

$8.59 lost per week.

5 weeks.

$8.59 x 5 = $42.95.

Hope this helps!

If not, I am sorry.

Answer:

The sum of the interior angles of any quadrilateral is 360°.

Answer:

Step-by-step explanation:

A quadrilateral is a polygon which has 4 vertices and 4 sides enclosing 4 angles and the sum of all the angles is 360°.

I'll give you an example with the square, it has 4 right angles, so the sum is 360 ° as in all quadrilaterals.

The range is from the maximum point into infinity that is [4, infty) and the vertex is at (0, 4)

The given graph is a parabola. It represents the graph of a quadratic equation.

From the shown graph, the parabola has a maximum point at (0, 4). This is also the vertex of the graph

The domain area values along the x-axis while the range lies on the y-axis. From the graph shown, the domain is [-2, 2] (x lies between -2 and 2)

The range is from the maximum point into infinity that is [4, infty)

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Answer:

3

Step-by-step explanation:

11(3)+2 = 6

also,

33-29 =

and

29 - 23 = 6

I take a guss, but I think its 3

i love robloox

               n n n nn

Answer:

Step-by-step explanation:

slope=(1-3)/(-2-(-5))

=-2/(-2+5)

=-2/3

Answer:

2000 tickets were sold

Step-by-step explanation:

40% can also be written as 0.40

800/ 0.40 = 2000 total tickets