3/5(1/2p + 2r) + 2p
please simplify!!!
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).
A good example of an algebraic expression is 3x² + 2xy + c.Any expression that can be converted into a rational fraction using the properties of the arithmetic operations is said to be rational (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions). In other terms, a rational expression is one that can be created using only the four arithmetic operations and the variables and constants.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] .
To learn more about algebraic expression visit:
https://brainly.com/question/19245500
#SPJ9
PLEASE HELP WITH THID QUESTIONS ASAPPP
Answer:
12
Step-by-step explanation:
16/4=4
4*3=12
Hope this helps!
PLEASE HELP 15 points
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
Write a difference quotient that best approximates the instantaneous rate of change of g at x=2.5.
A difference quotient that best approximates the instantaneous rate of change of g at x=2.5 is; -3
What is the Difference Quotient?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.
Read more about Difference Quotient at; https://brainly.com/question/21840322
#SPJ1
suppose you want to estimate the proportion of students at a large university that approve of the new health care bill. you take an srs of 200 of the 25,000 undergraduate students and an srs of 100 of the 5,000 graduate students.
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.
To learn more about the simple random sample and stratified random sample from the given link:
https://brainly.com/question/14470673
#SPJ4
please help with problem 21
Answer:
Step-by-step explanation:
25 monsters went to McSpooks Diner. They
each spent $57.18 on their meals. How much
in total did the group of monsters spend at
McSpooks Diner?
Answer:
1429.5
Step-by-step explanation:
The triangle O'P'Q' is a dilation of the triangle OPQ. What is the scale factor of the dilation?
104
-10 -8 -6
Pr
-4
-2
do
P
6
4
2
O
o
-2
-4
-6
8
6
00
10
10
Simplify your answer and write it as a proper fraction, an improper fraction, or a whole
number.
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
Add signs to make true:
3 3 3 3 3=6
(01.02 mc) solve for x: two thirds(x − 2) = 4x. a x = negative two fifths b x = negative five halves c x = two fifths d x = −2
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.
What is linear equation in one variable?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.
To know more about linear equation in one variable, here
https://brainly.com/question/85774
#SPJ4
The amount of money raised at a fundraiser is directly proportional to the number of attendees. The amount of money raised for 12 attendees is $300. How much money is raised for 75 attendees? $300 $1,875 $900 $2,775
The amount of money raised for 75 attendees will be $1875. The correct option is B.
What is an expression?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.
To know more about an expression follow
https://brainly.com/question/19735759
#SPJ1
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 grab your equation using the axes below
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.
Learn more about linear equation here
https://brainly.com/question/4074386
#SPJ9
Katherine has $460 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $362.68.
She buys 3 bicycle reflectors for $10.20 each and a pair of bike gloves for $12.54.
She plans to spend some or all of the money she has left to buy new biking outfits for $27.09 each.
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 number of apples in a fruit basket is
directly proportional to the number of
oranges. If there are 2 apples and 5 oranges
in Mary's basket, how many more apples are
there in a basket that contains 35 oranges?
Can A 3-kilogram bag of potting soil costs $6.95. What is the unit price, rounded to the nearest
cent?
biker bikes 2 1/4 miles in 15 min or 1/4 of an hour
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.
What are the intervals of increase and decrease for the absolute value function below?
1. Increase: x > 0, decrease: x < 0
2. Increase: x < 0, decrease: x > 0
3. Increase: y < 0, decrease: y > 0
4. Increase: y > 0, decrease: y > 0
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.
use a scalar projection to show that the distance from a point p1sx1, y1d to the line ax 1 by 1 c − 0 is
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]
To learn more about the scalar projection from the given link:
https://brainly.com/question/14411896
#SPJ4
if i have 3.6 pounds and their 1.42 per pound how much did i pay for the apples
Answer:
$5.11
Step-by-step explanation:
3.6 x 1.42 = 5.112
If a line, line segment, or ray is perpendicular to a plane, it is perpendicular to every line, line segment, or ray in the plane that intersects it.
c. If a line is perpendicular to a plane, then every plane containing the line is perpendicular to the given plane. If line a is perpendicular to plane P , what must also be true?
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.
What is a line?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.
What is a line segment?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.
What is a conditional statement?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.
Read more on conditional statement here: brainly.com/question/16951916
#SPJ1
-1/2=y-1 solve for y and I need to know how you solved it
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!
Consider a physical pendulum with length of 94.7 cm and mass of 166 g. if the pendulum was released from an angle less than 10o, then calculate the angular speed of the pendulum. (g = 9.80 m/s2)
Angular velocity of pendulum is 3.216 rad/s.
What is angular velocity?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]
To know more about angular velocity, visit:
https://brainly.com/question/20432894
#SPJ4
Simplify this expression and show ALL steps ( PLEASE HELPP )
-5(4) + (-40) divided by (-10)
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
(a) The area of a rectangular field is 7546 m².
If the length of the field is 98 m, what is its width?
Width of the field: m
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
9.
The Senior House Master of (SHS) invited the School's Volleyball players and Prefects on
duty to his office. 14 students altogether reported. 7 Volleyball players left his office, leaving
behind only the Prefects on duty. If 10 of them play Volleyball, find:
the number of students who were both prefects and Volleyball players;
those who were only Prefects.
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.
How many students are prefects?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
Find out more on school prefects at https://brainly.com/question/22532382
#SPJ1
how to solve? …………….
Answer:
6x + 9
3(2x + 3)
please correct me if I'm wrong
for a randomly selected worker, what is the approximate probability the bolt will be inserted in 19 minutes or less? round to the nearest whole percent.
The probability that the bolt will be inserted in 19 minutes or less is 0.8413.
How to calculate the probability?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.
Learn more about probability on:
brainly.com/question/6817058
#SPJ4
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?
Write an equation in slope-intercept form for the perpendicular bisector of the segment with the given endpoints. Justify your answer. (Lesson 5-1)
D(-2,4) and E(3,5)
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
To learn more about perpendicular bisector: https://brainly.com/question/24159921
#SPJ4
Find an equivalent ratio to 8:7. O a. 40:35 O b. 40:30 O c. 20:19 O d. none of the above
Answer
a. 40:35
Step-by-step explanation:
8 * 5 is 40 and 7 * 5 is
Lucinda has three packages of baseball cards. the first package has thirteen cards. the second package has twenty-six cards, and the third package has twenty-two cards. using front end estimation, what is the best estimate for the total number of baseball cards she has? a. 30 b. 40 c. 50 d. 60