Rewrite 120 + 400 using the GCF and factoring.

12(10 + 40)
20(10 + 2)
40(3 + 400)
40(3 + 10)

Pls help asap

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:

1429.5

Step-by-step explanation:

Answer

a. 40:35

Step-by-step explanation:

8 * 5 is 40 and 7 * 5 is

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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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.

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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The linear equation from the given statement is the N + F+11 = 2F.

According to the statement

We have to write the linear equation.

So, For this purpose, we know that the

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.

From the given information:

David has 11 shirts to fold. Let N be the number of shirts he would have left to fold after folding F of them. Write an equation relating and 2F.

Then

The number of shirts left = N

The number of the shirts which are folded = F+11

The total number of shirts = 2F

And then

The linear equation becomes :

N + F+11 = 2F

This the linear equation for the given statement.

So, The linear equation from the given statement is the N + F+11 = 2F.

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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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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:

-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:

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 :)

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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Answer: the scale factor is 5

Step-by-step explanation:

5 squares on the dilated shape and for the original shape it’s only 1 and the original shape is always going to be the denominator while the numerator is going to be the shape after it’s dilated so it’s 5/1 which equals 5

So THE ANSWER IS 5

Answer:

12

Step-by-step explanation:

16/4=4

4*3=12

Hope this helps!

The probability that the bolt will be inserted in 19 minutes or less is 0.8413.

It should be noted that the probability will be illustrated as:

P(X < x) = P[z < (x - u/sd)]

where

x = number

u = mean

SD = standard deviation

Therefore given the numbers, this will be:

P(x < 19) = P(z < (19 - 15)/4)

= P(z < 4/4) = P(z < 1)

= 0.8413

Therefore, the probability that the bolt will be inserted in 19 minutes or less is 0.8413.

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The mean time it takes for workers at a factory to insert a delicate bolt into an engine is 15 minutes. The standard deviation of time to insert the bolt is 4.0 minutes and the distribution of time is approximately Normally distributed. For a randomly selected worker, what is the approximate probability the bolt will be inserted in 19 minutes or less?

A difference quotient that best approximates the instantaneous rate of change of g at x=2.5 is; -3

We can define the average rate of change of a function g(x) in an interval [a, b] as:

r = [g(b) - g(a)]/(b - a)

Particularly, if we want to find an approximation of the rate of change for a particular value x', we can choose:

a < x' < b

Such that a and b are really close to x'.

Then if we want to find the instantaneous rate of change of g at x = 2.5, we need to find values of a and b really close to 2.5.

Looking at the graph, we can choose:

a = 2

b = 3

(are the two closer ones to 2.5)

Then the rate of change can be written as:

f'(x) = g(3) - g(2)]/(3 - 2)

f'(x) = (1 - 4)/1

f'(x) = -3

Thus, we can conclude that a good approximation of the instantaneous rate of change is -3.

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According to the question, srs is a simple random sample whose size consists of individuals from the population and chosen in such a way that every set of individuals has an equal chance to be sampled.

What is Stratified random samples?

For stratified random samples, initially classify the population into the groups of similar individuals which is called as “strata”. Later choose simple random samples and combine them to form a full sample.

As per question, srs of [tex]200[/tex] of the [tex]25000[/tex] undergraduate students and the srs of [tex]100[/tex] of the [tex]500[/tex] graduate students. This overall sample is a stratified sample.

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Step-by-step explanation:

(4h⁴)⁴ / (4h^-8)

remember, multiplying exponents means adding them. exponents of exponents means multiplying them.

and dividing exponents means subtracting them.

also, n^-a = 1/(n^a).

let's look at the numerator (top part) first :

(4h⁴)⁴ = 4^1×4 × h^4×4 = 4⁴×h¹⁶

now, for the denominator, the exponent -8 applies only to h. not to 4.

so,

1/(4h^-8) = h⁸/4

and so, the whole expression is then simplified

4⁴×h¹⁶ × h⁸/4 = 4³ × h²⁴

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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The simplified form of the algebraic expression is [tex]\frac{23}{10} p+\frac{6}{5} r[/tex] .

An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number).

Given expression is of the form:

[tex]\frac{3}{5} (\frac{1}{2}p+2r )+2p[/tex]

Now we will use the distributive property to expand the algebraic expression:

[tex]or, (\frac{3}{5} \times\frac{1}{2}p+\frac{3}{5} \times2r) +2p\\\\or,\frac{3}{10}p+\frac{6}{5} r+2p\\ \\or,\frac{3+20}{10} p+\frac{6}{5} r\\\\or,\frac{23}{10} p+\frac{6}{5} r[/tex]

Hence the simplified algebraic expression is  [tex]\frac{23}{10} p+\frac{6}{5} r[/tex] .

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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:

6x + 9

3(2x + 3)

please correct me if I'm wrong

Answer:

$5.11

Step-by-step explanation:

3.6 x 1.42 = 5.112

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.

Solution:

[tex]y = \frac{1}{2}[/tex]

Process of Solution:

1. Switch sides.

[tex]y-1=-\frac{1}{2}[/tex]

2. Add 1 to both sides.

[tex]y-1+1=-\frac{1}{2} +1[/tex]

3. Simplify.

[tex]y = \frac{1}{2}[/tex]

Hope this helps!