Determine the solutions of the equation:
|1/4x+7|-3=24
x= -136 and x = 136
x= -136 and x = 80
x=-112 and x = 80
x= -80 and x = 80

According to the question, the given data for the scalar projection calculation represent the point [tex]P1(x1,y1)[/tex] to the line [tex]ax1+by1+c=0.[/tex]

What is scalar projection?

Scalar projection refers to scalar coordinates in the cartesian coordinates. It is also the length of the vector projection. It is calculated with the help of the dot product with the unit vector direction. It always tells about the magnitude of the projection.

By using scalar projection, calculate the distance from the point [tex]P1[/tex] to the line.

Here,[tex](a, b)[/tex] is perpendicular and the equation can be written as

           [tex]by1 = -ax1-c[/tex]    

          [tex]y1 = -\frac{a}{b}x1-c[/tex]

For this the slope of the given equation can be written as: [tex]-\frac{a}{b}[/tex]

And the distance is : [tex]d = \frac{|ax1+by1+c|}{\sqrt{a2+b2} }[/tex].

Therefore, the calculated distance for the given equation is:[tex]d = \frac{|ax1+by1+c|}{\sqrt{a2+b2} }[/tex]

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Answer:

82 + -71 = 10

Hope this helps! <3

Based on the number of students invited to the office and the number of Volleyball students who left, the number of students who were both prefects and volleyball players are 3 students.

Those who are only prefects are 4 students.

To find the number of students who were both prefects and volleyball players, the formula is

= Number of volleyball players who left + Total number of volleyball players - Number of students called to office

= 7 + 10 - 14

= 3 students

Number of students who were just prefects:
= Number of students called - Number of students who left - Number of students who are prefects and volleyball players

= 14 - 7 - 3

= 4 students

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Answer:

[tex] \sf \large \: V = -1.5[/tex]

Step-by-step explanation:

Let's solve the equation step by step,

v=u+ at

V = 2 + -7(0.5)

V = 2 + -3.5

V = -1.5

Answer:

Should be 9 mph

Step-by-step explanation:

2.25 miles divided by .25 hours will give you a speed measured in miles per hour.

The statement which must also be true is that: since line a is perpendicular to line P, any plane containing line a is perpendicular to line P.

A line can be defined as a mark with length and direction, that is created by a point that is moving across a surface. Also, a line can vary in length, width, direction, curvature, and color.

A line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points and it typically has a fixed length.

A conditional statement can be defined as a type of statement that can be written to have both a hypothesis and conclusion. This ultimately implies that, a conditional statement typically has the form "if P then Q."

Where:

P and Q represent sentences.

From the given conditional statement, we can reasonably and logically deduce that if line a is perpendicular to line P, any plane that contains line a is perpendicular to line P.

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The correct option is a) x = negative two fifths. The value of x is obtained by solving it with rules of linear equation in two variable as x = -2/5.

A linear equation in one variable is an equation that has only one solution and is expressed in the form ax+b = 0, where a and b are two integers and x is a variable. 2x+3=8, for example, is a linear equation with a single variable.

Now, as per the given expression;

                                2/3(x -2) = 4x

Multiply both sides of equation by 3.

                                2(x - 2) = 12x

Simplifying;

                                2x - 4  = 12x

Subtract 2x on both sides of the equations.

                                -4 = 12x - 2x

Again Simplifying;

                               -4 = 10x

Divided by 10 on both sides

                                x = -4 / 10

                                x = -2/5

Therefore, the value of x is obtained as x = -2/5.

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Answer:

Equation: 2.50 + 3h = 13.00

Solution: h = 3.50

Step-by-step explanation:

Letting h be the cost of one hamburger:

[tex]2.50 + 3h = 13.00[/tex]

[tex]3h = 10.50[/tex]

[tex]h = 3.50[/tex]

So the cost of one hamburger is $3.50.

Answer:

$5.11

Step-by-step explanation:

3.6 x 1.42 = 5.112

Answer:

So I'm guessing the question is how much biking outfits she can buy?

She can buy 1, because she'll have 53.98 left over, and that is enough to buy 1 biking outfit,

Step-by-step explanation:

Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day :)

Answer:

6x + 9

3(2x + 3)

please correct me if I'm wrong

answer:

it has a solution

Answer: 24

Step-by-step explanation:

t=seconds. h=height

t=3

h=3+55t-16t^2

h=3+55(3)-16(3)^2

h=3+165-16*9

h=168-144

h=24 ft

The ball's height 3 seconds after it was kicked is 24 feet above the ground.

Given that a formula h = 3 + 55t-16t² describes a ball's height above the ground h, which has been kicked vertically upward from a height of 3 feet with an initial speed of 55 feet per second.

We need to find the height of the ball after 3 seconds.

To find the ball's height 3 seconds after it was kicked, we can use the formula provided:

h = 3 + 55t - 16t²

where h represents the height in feet and t represents the time in seconds.

To find the height after 3 seconds (t = 3), plug the value into the formula and calculate:

h = 3 + 55(3) - 16(3)²

Now, perform the calculations step by step:

h = 3 + 55(3) - 16(9)

h = 3 + 165 - 144

h = 24 feet

Hence the required height is 24 feet.

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Answer:

12

Step-by-step explanation:

16/4=4

4*3=12

Hope this helps!

The equation of the perpendicular bisector of the segment with the endpoints located at D(-2 , 4) and E(3 , 5) is y = -5x + 7

A perpendicular bisector of a segment is a line that divides the segment into two equal parts forming right angles at the point of intersection.

To get the perpendicular bisector of a segment, get the point of intersection of the two lines which is the midpoint of the segment.

midpoint (x , y) = [(x1 + x2)/2 , (y1 + y2)/2]

midpoint (x , y) = [(-2 + 3)/2 , (4 + 5)/2]

midpoint (x , y) = (1/2 , 9/2)

Get the slope of the perpendicular bisector of a segment by taking the negative reciprocal of the slope of the segment.

slope of segment = (y2 - y1)/(x2 - x1)

slope of segment = (5 - 4)/(3 - -2)

slope of segment = 1/5

slope of the perpendicular bisector = -5

Solving for the y-intercept, b, plug in the point (1/2 , 9/2) and the slope -5 to the slope-intercept form of the equation, y = mx + b.

y = mx + b

9/2 = -5(1/2) + b

b = 7

Setting up the equation in slope-intercept form, where m = -5 and b = 7.

y = mx + b

y = -5x + 7

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Answer

a. 40:35

Step-by-step explanation:

8 * 5 is 40 and 7 * 5 is

The correct answer is other measures of location need not be the same.

What is mean, mode, median and standard deviation?

When the group of numbers have the same mean then the other measures of location need not be the same. That means the standard deviation, median and mode should not be equal. All three widely used parameters that are mean, mode, median and standard deviation are the measure of central tendency.

If the given data has no outlier then mean value and the median value are closer to each other but the mode value is different. Similarly, standard deviation is calculated for the dispersion data. And it means when mean value is same then standard deviation will be different for a group of numbers.

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Angular velocity of pendulum is 3.216 rad/s.

In physics, the rotational velocity ( or ), also referred to as the angular frequency vector, is a pseudovector representation of how quickly an object's angular position or orientation varies over time (i.e. how quickly an object rotates or revolves relative to a point or axis). The pseudovector's direction is normal to the instantaneous plane of rotation or angular displacement, and its magnitude equals the rate at which the object is rotating or revolving. Traditionally, the right-hand rule is used to specify the direction of angular motion.

Orbital and spin angular velocities are the two forms of angular velocities.

For a small angle angular velocity of the pendulum is calculated as:

ω[tex]= \sqrt{\frac{g}{l} }[/tex]

Here, g= gravity acceleration and l = pendulum's length.

Conversation of unit of length are,

l=94.7 cm = 94.7 cm * ([tex]\frac{10^{-2}m}{1cm}[/tex]) = 0.947 m

Substitute l = 0.947 m and g = 9.80 [tex]m/s^2[/tex] in the expression ω[tex]= \sqrt{\frac{g}{l} }[/tex]

ω[tex]= \sqrt{\frac{9.80m/s^2}{0.947m} } = 3.216[/tex]

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The equations that are equivalent are B×10p = 2 and D×p = 20.

Given, For $5.00, Jamie purchased a notebook and a box of pencils.

10 pencils are contained in a box, and the notepad costs $3.00.

The price of one pencil can be calculated using the equation 3+10p=5.

According to the question:

3 ₊ 10p = 5

10p = 5 ₋ 3

10p = 2

p = 2/10

p = 0.2

equations can be :

B × 10p = 2 and D × p = 0.20

Hence we get the equations as: B × 10p = 2 and D × p = 0.20

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Answer:

1429.5

Step-by-step explanation:

Answer:

-16

Step-by-step explanation:

Use pemdas:

1. -5 times 4 is -20

2.  -40 divided by -10 is 4

3. -20 plus 4 is -16

Answer:

77m

Step-by-step explanation:

Area of rectangle = L x W

7536m² = 98 x W

(Divide both sides by 98 to get W)

W = 7536m ÷ 98m

W = 77m

Answer:

1814.85 N

Step-by-step explanation:

Weight = mass * acceleration of gravity

Jayden's weight = 185 * 9.81 = 1814.85 N

Answer:

Step-by-step explanation:

The amount of money raised for 75 attendees will be $1875. The correct option is B.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given that the money raised for 12 attendees is $300. The money raised for 75 attendees will be calculated as below:-

12 attendees = $300

1 attendees = $300 / 12

75 attendees  =  $300 x 75 / 12

75 attendees  = $1875

Therefore, the amount of money raised for 75 attendees will be $1875. The correct option is B.

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Answer:

Step-by-step explanation:

The function interval is said to be positive if the value of the function f (x) increases with an increase in the value of x. In contrast, the function interval is said to be negative if the value of the function f (x) decreases with the increase in the value of x.