The simplified form of 4.5p (2 - 0.2p) is option A 9p - 0.9p²
Given,
The expression: 4.5p (2 - 0.2p)
We have to simplify the expression:
Simplification:A mathematical expression is simplified when it is replaced with a simpler, typically shorter, equivalent statement.
Difference between simplification and solving:They are different in a way that extends the distinction between expressions and equations. Either equations or expressions can be simplified. Making the math language simpler entails shortening it. Finding the value or values that make the equation, or math sentence, true, is the process of solving.
That is,
4.5p (2 - 0.2p)
Open the bracket and do the multiplication:
(4.5p × 2) - (4.5p × 0.2p)
= 9p - 0.9p²
That is, the simplified form of the expression 4.5p (2 - 0.2p) is 9p - 0.9p².
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2. Find and simplify the product of f and g *
given the functions f (x)
; g(x) = -²
=
x+2
(2 Points)
The product of the functions f(x) and g(x), where the functions f(x) = [tex]x+2[/tex] and g(x) = [tex]-x^{2}[/tex] is
As per the given question statement, we are supposed to find and simplify the product of the functions f(x) and g(x), where the functions f(x) = [tex]x+2[/tex]and g(x) = [tex]-x^{2}[/tex].
Let's assume [tex]m(x)[/tex] be the product of the functions [tex]f(x)[/tex] and [tex]g(x)[/tex]
So, [tex]m(x) = f(x) * g(x)\\m(x)= (x+2)*(-x^{2} )\\m(x)=-x^{3} -2x^{2}[/tex]
Therefore the product of the functions f(x) and g(x), where the functions f(x) = [tex]x+2[/tex]and g(x) = [tex]-x^{2}[/tex] is [tex]m(x)=-x^{3} -2x^{2}[/tex]
This question is a classic example of how to solve functions using different mathematical operations and using the concept of algebraic expressions.
Algebraic Expressions: An algebraic symbol or set of symbols that includes one or more integers, variables, and arithmetic operations.To learn more about algebraic expressions, click on the link given below:
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A kinara is a candle holder used during Kwanzaa celebrations. The graph shows the
number of kinaras, rounded to the nearest 500, an online store sold each year for 15
years. A line of fit is drawn to show the trend of the data. What does the slope of the line
represent?
Answer:C
Step-by-step explanation:
What is the distance between "-17" and "-6"
Answer:
11
Step-by-step explanation:
Answer:
11
Step-by-step explanation
17
-6
=11
Ordered: 130 mg. Available: 1 gr/tablet. How many tablets should be given? ________
Answer:
2
Step-by-step explanation:
1gr=100mg
130-100=30
No tablets should be given since the ordered quantity of 130 mg is less than the available quantity per tablet of 1 g.
How many tablets should be given?We have the following data:
Ordered amount: 130 mg
Available amount per tablet: 1 g
To decide the number of tablets to be given, we have to be make sure the units are steady. Let's change over the ordered amount to grams:
130 mg = 130/1000 g = 0.13 g
Presently, we are able calculate the number of tablets:
Number of tablets = Ordered amount / Available amount per tablet
Number of tablets = 0.13 g / 1 g = 0.13 tablets
Since we cannot administer a fraction of a tablet, we round the result to the closest whole number. In this case, 0.13 is less than 0.5, so we round down:
Number of tablets to be given = tablets
Hence, no tablets ought to be given since the ordered amount of 130 mg is less than the available amount per tablet of 1 g.
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22. The area of a floor that is fourteen and one-half feet wide is two hundred thirty-nine and one-fourth square feet. Find the perimeter of the floor.
The perimeter of the floor is found to be 62 feet.
What is defined as the rectangle?A rectangle is a closed two-dimensional shape with four sides, four corners, and four right angles (90°).
A rectangle's opposite sides are equal as well as parallel. Because a rectangle is a 2-D shape, it has two dimensions: length and width. The length of the rectangle is the longer side, and the width is indeed the shorter side.Now, as per the given question;
The area of the rectangular floor is given as two hundred thirty-nine and one-fourth square feet.
Thus,
A = 239.25 feet
The width is fourteen and one-half feet.
Thus,
W = 14.5 feet
The formula for area is;
A = L×B (L is the length)
Put the values;
239.25 = L×14.5
L = 239.25/14.5
L = 16.5 feet
The rectangular perimeter is;
P = 2(L + B)
P = 2(16.5 + 14.5)
P = 62 feet
Therefore, the perimeter of the rectangle floor is found to be 62 feet.
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77. What is the circumference of the larger circle
shown above in terms of x?
A. 10 π x
B. 10 π +x
C. 10 π +2x
D. 10π+ 2πx
[tex]\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=5+x \end{cases}\implies C=2\pi (5+x)\implies C=10\pi +2\pi x[/tex]
One number is 14 less than another. If their sum is increased by seven, the result is 85. Find the numbers.
Answer: 32, 46
Step-by-step explanation:
a=number 1. b=number 2
a=b-14
a+b+7=85
b-14+b+7=85
b+b-14+7=85
2b-7=85
2b=92
b=46
a=46-14
a=32
Answer:
Step-by-step explanation:
the equation to find this is
x+(x+14)+7=85
first minus the 7
X+(x+14)+7-7= 85-7
x+(x+14)=78
78÷2 = 39
42+36
Please help! 10 points. If u don’t know the answer don’t answer please!
Answer: The answer is C
Step-by-step explanation: Bro I'm in 8th grade rn and I know the answer XD my IQ is 137 :)
Answer:b
Step-by-step explanation:becuase -2x times 6x = -12x
then your done with that part so then multiply 7x7 and that's 49 so its
-12x+49
HELP WITH THIS MATH QUESTION PLEASE! I WILL GIVE BRAINLYEST!!
Determine if each sequence below is arithmetic or not.
a. 200, 40, 8
b. -6,-3,0, 3
c. Danielles parents have offered her a way to earn her allowance each week. She would get paid $30 each week. Does the amount of money Danielle has earned on the nth week represent an arithmetic sequence?
d. The price of a stock on day n of the year
Answer:
I think the answer would be the letter b
Gwen has loyalty card for a store that gives her a discount of 5% off the marked price of items. Office Chair $800, Acer Laptop $4580.
(a) How much will she pay if she bought the two items above?
(b) The store buys the chairs at $1 530 for two. Show whether the store made a profit on the one chair from Gwen’s Purchase.
Construct a parallelogram PQRS such that PQ = 8.1 cm, QR = 6.9 cm and the diagonal QS = 10.4 cm. Measure and write down the length of the diagonal PR.
Answer:
10.4 it is the correct answer please mark me as a brainlist
Use the hundredth grids below to answer the questions. The first two hundredth grids show Sophia's work. The second two hundredth grids show Aiden's work.
This image shows Sophia's work. One whole 10-by-10 grid and 2 columns and 5 squares on a second grid are shaded blue. On the second grid, the remaining 5 squares in the third column, 3 more columns, and 5 more squares are shaded brown.
This image shows Aiden's work. One whole 10-by-10 grid and 2 columns and 5 squares on a second grid are shaded blue. On the second grid, 4 squares in the third column are shaded brown.
Part A
Which student correctly models the problem 1.25 + 0.4. Type your answer in the box.
Sophia
Part B
What is the correct answer for 1.25 + 0.4?
1.65
Part C
Explain the errors made by the incorrect student. Refer back to the models and use equations to support your explanation.
Answer:
Aiden got the question wrong because he added four squares instead of four columns. Aiden confused 0.4 with 0.04, using 4 ones instead of 4 tens.
Im sorry if this is confusing i hope it helped :)
Kim multiplied 8 x 0.952 and got 76.16. How can you estimate to show that kim answer is incorrect
can you sum 58.91 570 42,769 994.8
Answer: Yes, i think. you add 0's to 58.91 -----> 58.910. 570-------->570.000. 42,769-------->42,769.000. 994.800. to line them perfectly. greatest are always on top smallest are in the bottom
The sum of numbers 58.91, 570, 42,769, 994.8 will be
⇒ 44392.71
What is Addition?
The process of combining two or more numbers is called the Addition.
Given that;
The number are,
58.91, 570, 42,769, 994.8
Now,
The sum of numbers 58.91, 570, 42,769, 994.8 is,
⇒ 58.91 + 570 + 42,769 + 994.8
⇒ 44392.71
Thus, The sum of numbers 58.91, 570, 42,769, 994.8 will be
⇒ 44392.71
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A list of needed materials calls for one five-pound pack of deck screws. You have three leftover packs. Two of them are 1/4 full, and the third pack is 1/3 full. Expressed as a fraction, what part of a full 5-pound pack of nails do you have?
Based on the fact that there are three leftover packs, the part of the 5-pound pack of nails that you have is 5/6
What part of the pack do you have?To find the part of the full 5-pound pack of nails that you have, you need to add up all the fractions of the leftovers that you have.
The part of the full 5-pound pack that you have is:
= 1/4 + 1/ 4 + 1/3
= 3/12 + 3/12 + 4/12
= 10/12
In the simplest term, this is:
= 5/6
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Evaluate 3x - 7 when x = 4
Answer:
5
Step-by-step explanation:
3x-7
=3×4-7
=12-7
=5..........
How much it’s 27+ 0.185
Answer:
27.185
Step-by-step explanation:
The vertical position y (in feet) of a rock t seconds after it was dropped from a cliff is given by the formula y equals short dash -16 t squared plus 4 t plus 380. The base of the cliff corresponds to y = 0. After how many seconds will the rock hit the ground at the base of the cliff?
The seconds that it will take the rock hit the ground at the base of the cliff is 5 seconds
How to calculate the value?Based on the information given, it should be noted that the expression given is:
y = -16t² + 4t +380
We have to divide through by 4. Therefore,
y = -4t² + t + 95
y = -4t² + 20t - 19t + 95
y = -4t(t - 5) - 19(t - 5)
t - 5 = 0
t = 0 + 5
t = 5
The time taken will be 5 seconds.
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Select all the products that are equivalent to 1/6
A. −3/4⋅(−2/9)⋅1/2
B. −3/2⋅(−2/9)⋅1/2
C. −1/2⋅(−2/3)⋅1/2
D. 1/2⋅(−2/9)⋅1/2
E. 1/2⋅(−5/6)⋅(−2/5)
B, C, and E are the products equivalent to 1/6
We have been given five different products and we have to find out which of them are equivalent to 1/6. So,
(-3/4)*(-2/9)*(1/2) => 6/72 => 1/12(-3/2)*(-2/9)*(1/2) => 6/36 => 1/6(-1/2)*(-2/3)*(1/2) => 2/12 => 1/6(1/2)*(-2/9)*(1/2) => -2/36 => -1/18(1/2)*(-5/6)*(-2/5) => 10/60 => 1/6Here we observe that the product of B, C, and E after solving them is equivalent to 1/6 whereas, the product of A and D is 1/12 and -1/18 respectively.
Hence, We get that the product for the numbers
(-3/2)*(-2/9)*(1/2), (-1/2))*(-2/3)*(1/2), and (1/2)*(-5/6)*(-2/5)Which are Options B, C, and E equivalent to 1/6
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Hey I need help please help
The slope of the linear function shown in the graph is of 2, as:
Run = 2.Slope = rise/run = 4/2 = 2.What is a linear function?A linear function is modeled according to the following rule:
y = mx + b
In which:
m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis, that is, when x = 0.For this problem, we want to find the slope given two points of the function, which are (2,4).
For the calculation, we have that:
The rise is the change in y.The run is the change in x.Hence:
The rise is of 4 - 0 = 4.The run is of 2 - 0 = 2.The slope is of 4/2 = 2.More can be learned about linear functions at https://brainly.com/question/24808124
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Brody's age is 3 years less than twice Trinity's age? The sum of their ages is 30.
Answer: Brody's Age is 19 and Trinity's age is 11
Step-by-step explanation:
x = Trinity's age
2x-3= Brody's age
The sum of the ages is 30, so
x + (2x-3) = 30
3x - 3 = 30
add 3 to both sides 30 turns into 33 so,
3x = 33
divide by 3 both sides
x = 11 which is trinity's age and plug x into 2x - 3 which is 19 so that's Brody's age.
What is the domain of the function y = square root x+6 -7?
Answer:
-6 ≤ x < ∞
Step-by-step explanation:
You want the domain of the function y = √(x+6) -7.
DomainThe domain of a function is the set of x-values for which the function is defined. On a graph, it is the horizontal extent of the graph.
The square root function is undefined for negative arguments, so that limits the domain of the given function:
x+6 ≥ 0
x ≥ -6 . . . . . domain of the given function
__
Additional comment
When the domain is written in interval notation, both the left and right ends of the interval must be specified.
[-6, ∞)
The square bracket identifies -6 as being part of the domain. The parenthesis is used with ∞, because that number has no specific value.
[tex]\left|16x\right|\le 8[/tex]
Please help me with this, and thank you.
Answer:
-1/2 ≤ x ≤ 1/2 or x∈ [- 1/2, 1/2]Step-by-step explanation:
|16x| ≤ 8|16x/16| ≤ 8/16|x| ≤ 1/2x ≤ 1/2 or x ≥ - 1/2Combination of two inequalities above:
-1/2 ≤ x ≤ 1/2Or interval notation:
x∈ [- 1/2, 1/2]The sum of the ages of Steve and Ali is
three times the difference of their ages.
What is the ratio of Ali's age to Steve's
age if Ali is older?
The ratio of Ali's age to Steve's is 2 to 1.
How to find the ratio of Ali age to Steve age ?The sum of the ages of Steve and Ali is three times the difference of their ages.
Therefore,
let
x = age of Steve
y = age of Ali
Hence,
x + y = 3(y - x)
x + y = 3y - 3x
Therefore,
x + 3x = 3y - y
4x = 2y
divide both side by 2
4x / 2 = 2y / 2
2x = y
The ratio of Ali's age to Steve's is 2 to 1.
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PLEASE HELP !?!????!?
Answer: Supplementary Angles
Step-by-step explanation:
Supplementary angles are a pair of angles whose sum is 180°. 45° and 135° add up to 180°. Therefore, the answer is supplementary angles.
ASAP Please help and thank you!
Charles, age 45, would like to determine how much life insurance to purchase using the human life value approach. He assumes his average annual earnings will remain at $40,000. Of this amount, $20,912 is available annually for the support of his family. Charles will generate this income for 24 more years and he believes that 5.37 percent is the appropriate interest (discount) rate. What is Charles' human life value? (Round your answer to 2 decimal places)
Using it's formula, it is found that Charles' human life value is of $26,951.39.
What is the human life value formula?The human life value formula(HLV) is given by the following multiplication:
HLV = Annual Expenses x Number of Years x Interest Rate.
For this problem, we have that:
$20,912 is available annually for the support of his family, hence the annual expenses are of $20,912.Charles will generate this income for 24 more years, hence the number of years is of 24.As stated in the problem, the interest rate is of 5.37%, hence, as a decimal, is of 0.0537.Hence, applying the formula, we have that Charles' human life value is found as follows:
HLV = 20912 x 24 x 0.0537
HLV = $26,951.39.
Charles' human life value is of $26,951.39.
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two investments totaling $28,000 produce annual income of $1435. One investment yields 9% per year, while the other yields 2% per year. How much is invested at each rate
The investment amount at 9% rate is $12500 and the investment
amount at 2% rate is $15500
What is mathematical expression?
A mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Let x be the amount invested at 9% rate.
And (28000−x) be the amount invested at 2% rate.
The total annual income is $1435
Let us find the amount invested at 9% rate:
x9%+2%(28000−x)=1435
9%+2%(28000−x)=1435
0.09x+0.02(28000−x)=1435
0.09x+560−0.02x=1435
0.09x−0.02x=1435−560
0.07x=875
x=875/0.07
x=12500
Let us find the investment amount at 2% rate:
⇒28000−x
⇒28000−12500
⇒15500
Therefore, the investment amount at 9% rate is $12500 and the investment amount at 2% rate is $15500.
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H=at-0.25vt*, solve for a
Yu Yan competes in a sprint triathlon. The race consists of three parts: a 0.5-mile swim, a 12.4-mile bike ride, and a 3.1-mile run. a. Yu Yan completes the swim portion of the sprint triathlon in 25 minutes. What is her average swimming speed in miles per minute?
The average swimming speed of Yu Yan is 0.02 miles per minute.
We are given that:
Yun Yan needs to swim 0.5 miles in the race.
She completed it in 25 minutes.
We need to find the average speed of Yu Yan in swimming in meter / minute.
We will do this by dividing the number of miles that she needed to swim with the number of minutes she took to complete it.
Average swimming speed = 0.5 miles / 25 minutes
Average swimming speed = 0.02 miles / minute
Therefore, the average swimming speed of Yu Yan is 0.02 miles per minute.
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Mayerlin wants to ride her bicycle 56 miles this week. She has already ridden 8 miles.
If she rides for 6 more days, what is the average number of miles she would have to
ride each day to meet her goal?
Please help!
if in the next 6 days she rides an average of 8 miles per day, she will meet her goal.
What is the average number of miles she would have to ride each day to meet her goal?We know that Mayerlin wants to ride her bicycle for 56 miles this week, and she already has ridden 8 miles, so the distance left is:
56mi - 8mi = 48mi
Now, to find the average distance that she needs to ride each day in order to meet her goal, we need to take the quotient between the distance left and the number days that she has left (6 days), then we will get:
D = 48mi/6 = 8mi
This means that if in the next 6 days she rides an average of 8 miles per day, she will meet her goal.
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