The equivalent expression is -4m + 10n + 10
What are algebraic expressions?It is important to know that algebraic expressions are described as expressions that are composed of terms, variables, constants, factors and coefficient of variables.
These algebraic expressions are also made up of mathematical operations.
These operations includes;
AdditionBracketParenthesesDivisionSubtractionMultiplicationNote that equivalent expressions have the same solution, we have;
−(4m - 0- 2n - 5. 5)
expand the bracket, we have
-(4m - 10n - 10)
remove the parentheses
-4m + 10n + 10
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what is the volume of the solid, if the length is 4 centimeters, the width is 8 centimeters and the height is 12 centimeters?
Answer:
384 cm^3
Step-by-step explanation:
the volume formula:
V = a*b*c,
where a - length, b - width, c - height
so, the volume of the solid is V = 4*8*12 = 384 cm^3
The volume of the solid, if the length is 4 centimeters, the width is 8 centimeters, and the height is 12 centimeters is 384 cm³.
To find the volume of the solid, we need to multiply the length, width, and height together. So, the volume of the solid is:
V = l x w x h
V = 4 cm x 8 cm x 12 cm
V = 384 cm³
Therefore, the volume of the solid is 384 cubic centimeters (cm³).
To find the volume of a solid with given dimensions, you can use the formula for the volume of a rectangular prism, which is Volume = Length × Width × Height. In this case, the length is 4 centimeters, the width is 8 centimeters, and the height is 12 centimeters.
Now, let's plug these values into the formula:
Volume = (4 cm) × (8 cm) × (12 cm)
By multiplying these numbers together, you'll get the volume of the solid:
Volume = 384 cubic centimeters (cm³)
So, the volume of the solid with the given dimensions is 384 cm³.
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How do I solve this?
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{y}\\ a=\stackrel{adjacent}{1}\\ o=\stackrel{opposite}{1} \end{cases} \\\\\\ y=\sqrt{ 1^2 + 1^2}\implies y=\sqrt{ 1 + 1 } \implies y=\sqrt{ 2 } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=\sqrt{a^2 + o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{x}\\ a=\stackrel{adjacent}{\sqrt{2}}\\ o=\stackrel{opposite}{13} \end{cases} \\\\\\ x=\sqrt{ (\sqrt{2})^2 + 13^2}\implies x=\sqrt{ 2 + 169 } \implies x=\sqrt{ 171 }\implies \boxed{x=3\sqrt{19}}[/tex]
Which of the following points is NOT a solution to the inequality
4х - у < 5?
A:(-4-1)
B:(1,5)
C:(2,3)
D:(-5,0)
The incorrect solution to the inequality is C ( 2 , 3 )
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
4x - y < 5
On simplifying , we get
Let the point be represented as C ( 2 , 3 )
Substituting the values in the inequality , we get
4 ( 2 ) - 3 < 5
8 - 3 < 5
5 is not less than 5
Hence , the point C ( 2 , 3 ) is not a solution
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What is 3/658 as a percent?
Answer: .46%
Step-by-step explanation:
=.00456 = .46% move decimal to right 2 times to convert to percent or x100
Diana uses 30 g of coffee beans to make 48 fluid ounces of coffee. We guess, she makes 96 fluid ounces coffee. How many grams of coffee does beans does Diana use when she has visitors?
Answer:
60g
Step-by-step explanation:
Okay, the first ratio we have is 30:48 (because she uses 30g of coffee beans to make 48 fluid oz).
To find how many coffee beans she uses for 96 fluid oz we need to find the unit rate.
To find the unit rate you divide the number by the greatest common factor of both numbers. The GCF of both numbers is 6 so we divide 30 and 48 by 6. We get the unit ratio of 5:8.
Now we can solve it.
We can solve the equation of [tex]\frac{x}{96} =\frac{5}{8}[/tex].
To solve this equation we need to multiply 96 by [tex]\frac{5}{8}[/tex]. Doing this gives us our answer of 60.
I went to the shop and brought some groceries for my mum. They cost 29. 65. Mum gave me 40. 0. How much change did i get ?
The change amount received after brought some groceries of amount $29.65 is equal to $10.35.
Amount of money given by Mum = $40.0
Cost of all the groceries is equal to $29.65
To find out how much change you received,
Subtract the cost of the groceries from the amount of money your mum gave you.
⇒ Amount received = Amount given - Cost of groceries
Substituting the given values, we get,
⇒ Amount received = $40.0 - $29.65
⇒ Amount received =$10.35
Therefore, after paying the amount of groceries the total changed received is equal to $10.35
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Write down in terms of n, an expression for the nth term
of the following sequences:
a) 4 1 -2 -5 -8
b) -7 -12 -17 -22 -27
Answer:
a) -3n + 7
b) -5n -2
Step-by-step explanation:
a) 4 1 -2 -5 -8
the difference = -3
the -3 times table = -3, -6, -9, -12 etc
from -3 to 4 we add 7
answer = -3n + 7
check = -3(4) + 7 should give -5 (because -5 is the 4th term in the sequence)
b) -7 -12 -17 -22 -27
the difference = -5
-5 times table = -5, -10, -15, -20
from -5 to -7 we subtract 2
answer = -5n -2
check = -5(5)-2 should give -27 (because -27 is the 5th term in the sequence)
A plane is at Manchester, which is 170km north of Worcester. The plane flies in a straight line for 230km and lands in Cambridge, which is directly east of Worcester.
Show this information in a diagram.
Use your diagram to find the bearing of Manchester from Cambridge.
The bearing of Manchester from Cambridge is 270⁰.
What is bearing?Bearing refers to the direction or angle between two points, usually measured in degrees, that indicates the horizontal angle between a reference point or line and a target point or object.
Bearing is typically expressed as an angle measured clockwise from north, which is known as "true north" or "geographic north".
The bearing of Manchester from Cambridge is the angle made by the plane from Cambridge back to Manchester.
From the diagram the bearing of Manchester from Cambridge is 270⁰.
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Geometry! Please answer
Answer:
A person travels in one complete rotation while riding on a Ferris wheel is 98.596 in terms of pi
Step-by-step explanation:
As we know the formula of circumference of Circle have the value of 2*3.14(pi)*r (radius of the circle), and2r=d (diameter of the circle), so to get the value of r we have to divide 78.5 from 2 to get 15.7 which is radius of circle. so as the person travels in one complete rotation while riding on a Ferris wheel therefore the calculation is done usually considering the above formula, as we apply the formula to the given problem we will get that 2* 3.14* 15.7 = 98.596.
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A jar of olives had a circumference of 11. 99 cm. What was the approximate diameter of the jar?
If the jar of olives had a circumference of 11. 99 cm, the approximate diameter of the jar is 3.82 cm
The circumference of a circle is given by the formula C = 2πr, where C is the circumference, π is the constant pi (approximately equal to 3.14), and r is the radius. The diameter is twice the radius, so we can also write the formula as C = πd, where d is the diameter.
In this case, the circumference is 11.99 cm, so we can set up the equation
11.99 = πd
To solve for d, we can divide both sides by π
d = 11.99/π
Using a calculator, we get
d ≈ 3.82 cm
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Determine whether each function represents X potential growth or decay select the correct option for each function.
Please help me
2x
ƒ(x) = ( 1 ) ²*
f(x) = (7)x-¹
3x
f(x) = (1.3) ³x
f(x) = (0.8)*
2x
f(x) = (-²)*
2
Growth Decay
0
0
0
0
O
O
Growth Decay
2x, ƒ(x) = (1)²*, 3x, f(x) = (1.3)³x - Growth
f(x) = (0.8)*2, f(x) = (-²)*2 - Decay
(The functions are categorized as either representing growth or decay.)
Growth Decay
2x - Growth (The function 2x represents exponential growth because as x increases, the value of 2x also increases.)
ƒ(x) = (1)²* - Growth (The function ƒ(x) = (1)² represents exponential growth because any number raised to the power of 2 will always be positive.)
f(x) = (7)x-¹ - Decay (The function f(x) = (7)x-¹ represents exponential decay because as x increases, the value of (7)x-¹ decreases.)
3x - Growth (The function 3x represents exponential growth because as x increases, the value of 3x also increases.)
f(x) = (1.3)³x - Growth (The function f(x) = (1.3)³x represents exponential growth because as x increases, the value of (1.3)³x also increases.)
f(x) = (0.8)*2 - Decay (The function f(x) = (0.8)*2 represents exponential decay because any number raised to the power of 2 will always be positive, and multiplying by 0.8 reduces the value.)
f(x) = (-²)*2 - Decay (The function f(x) = (-²)*2 represents exponential decay because any number raised to the power of 2 will always be positive, but the negative sign in front indicates a decay.)
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1 point
Calculate the mean and mean absolute deviation of these two data sets and use that to compare the two sets of data.
Set A: 4, 6, 7, 8,5,6
Set B: 5, 7,4,8,9,9
Set B has a lesser average and less consistent data values than Set A.
Set B has a greater average but has less consistent data values than Set A
Set B has a lesser average and more consistent data value than Set A.
Set B has a greater average and is more consistent data values than Set A.
Answer:
Step-by-step explanation:
professor oger must choose between an extra writing assignment and an extra reading assignment for the upcoming spring break. for the writing assignment, there are two essay topics to choose from and three different mandatory lengths (30 pages, 35 pages, or 40 pages). the reading topic would consist of one scholarly biography combined with one volume of essays. there are seven biographies and two volumes of essays to choose from. how many choices does she have?
The total number of options is therefore given by 6 + 15 = 21 options.
The number of options for selecting from two essay subjects and three distinct required lengths are provided by:
[tex]{}^{2}C_1\times{}^{3}C_1=2\times3=6[/tex]
As a result, he has 20 options for the writing task.
For the reading assignment, the number of options from three volumes of essays and five biographies are provided by:
5 x 3 = 15
The total number of options is therefore given by 6 + 15 = 21 options.
Assignment refers to a task or a piece of work assigned to someone, usually by a teacher, professor, or employer. In the academic context, assignments are a way for instructors to evaluate students' understanding of course material and their ability to apply it in a given scenario. Assignments can take different forms, such as essays, research papers, presentations, or group projects.
Assignments can have a significant impact on a student's grade, so it is important for students to take them seriously and submit them on time. They require planning, research, critical thinking, and organization skills to complete successfully. To ensure success, students should carefully read and follow the assignment instructions, use reliable sources, and adhere to the designated formatting and citation styles.
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What is the area of the shaded region?
Answer:
shaded area = 372.115 m²
Step-by-step explanation:
the shaded area is calculated as
area of outer Δ - area if inner Δ
area of outer = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
= [tex]\frac{1}{2}[/tex] × 35.4 × 32.3
= 17.7 × 32.3
= 571.71 m²
area of inner = [tex]\frac{1}{2}[/tex] × 20.9 × 19.1
= 10.45 × 19.1
= 199.595 m²
then
shaded area = 571.71 - 199.595 = 372.115 m²
PLEASE HELP ME I REALLY NEED TO GET MY GRADE UP I INCLUDED THE GRAPH WITH THE QUESTION!!!
Graph f(x) = -2/3x -3
Use the line tool and select two points to graph the line.
The tables represent the points earned in each game for a season by two football teams.
Eagles
3 24 14
27 10 13
10 21 24
17 27 7
40 37 55
Falcons
24 24 10
7 30 28
21 6 17
16 35 30
28 24 14
Which team had the best overall record for the season? Determine the best measure of center to compare, and explain your answer.
Eagles; they have a larger median value of 21 points
Falcons; they have a larger median value of 24 points
Eagles; they have a larger mean value of about 22 points
Falcons; they have a larger mean value of about 20.9 points
Falcons had a more effective overall record because of the higher median. Thus, the answer is option B.
The median is usually used for the comparison of two data sets instead of the mean, as it is not affected by outliers.
Compare the total points earned by each team.
The Eagles data set is given below:
3, 7, 10, 10, 13, 14, 17, 21, 24, 24, 27, 27, 37, 40, 55.
As the data set has an odd cardinality, the median is the middle element, therefore it is for:
21.
For the Falcons, we use the same approach and obtain a median about:
24.
Therefore, we can say that the Falcons had a more effective overall record because of the higher median and the best measure of center to compare would be mean.
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How many degrees is 1/18 of a semicircle?
Answer:
Step-by-step explanation:
A semi-circle has an angle of 180 degrees. So 1/18 of 180 gives 10 degrees as the answer
Jeremy tosses a fair die that has five sides labeled 1-5.
Part A
What is the probability that Jeremy rolls a 5?
A 0%
® 5%
© 20%
© 25%
Part B
What is the probability that Jeremy rolls a 3 or 5? Represent your probability as a decimal.
Answer:
PARTE A:
20%
PARTE B:
la probabilidad de que Jeremy saque un 3 o un 5 es 2/5 o 0,4 (40%) como decimal.
Step-by-step explanation:
find the volume of a pyramid with a square base, where the perimeter of the base is 10.7 ft 10.7 ft and the height of the pyramid is 9.8 ft 9.8 ft. round your answer to the nearest tenth of a cubic foot.
The volume of the pyramid is approximately 105.8 cubic feet.
To calculate the volume of the pyramid, we can use the formula V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid. Since the base of the pyramid is a square, we can use the formula for the area of a square, which is A = s², where s is the length of a side of the square.
Given that the perimeter of the base is 10.7 feet, we can calculate the length of each side of the square by dividing the perimeter by 4: s = 10.7 ft / 4 = 2.675 ft. Therefore, the area of the base is B = s² = 2.675²= 7.16 square feet.
Now we can plug in the values for B and h into the formula for the volume of the pyramid:
V = (1/3)Bh = (1/3) * 7.16 * 9.8 = 105.8 cubic feet.Therefore, the volume of the pyramid is approximately 105.8 cubic feet, rounded to the nearest tenth of a cubic foot.
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what is the rule for the nth term of the geometric sequence if the third term is 96 and the fifth term is 1,536?
The rule for the nth term of the geometric sequence is: [tex]an = 6 * 4^{(n-1)[/tex]
The rule for the nth term of a geometric sequence can be found using the third and fifth terms of the sequence. In this case, the rule is a = 24 and r = 4.
To find the rule for the nth term of a geometric sequence, we use the formula:
an = a1 *[tex]r^{(n-1)[/tex]
where an is the nth term, a1 is the first term, r is the common ratio, and n is the term number.
Given that the third term is 96 and the fifth term is 1,536, we can write two equations:
a * r² = 96
a *[tex]r^4[/tex]= 1536
Dividing the second equation by the first equation, we get:
r² = 16
Taking the square root of both sides, we get:
r = 4 (since r cannot be negative in a geometric sequence)
Substituting r = 4 into either of the two equations, we get:
a * 16 = 96
a = 6
Therefore, the rule for the nth term of the geometric sequence is:
[tex]an = 6 * 4^{(n-1)[/tex]
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sid pays 10.75 for 2.5 pounds of rib ribeye steak. What is the price per pound for rib eye steak.
The price per pound of rib eye steak as per the $10.75 paid by Sid for 2.5 pounds of rib ribeye steak is equal to $4.30.
Amount paid by Sid for rib ribeye steak is equal to $10.75
To find the price per pound of rib eye steak,
we need to divide the total price by the weight in pounds.
Price per pound = Total price / Weight in pounds
In this case, Sid paid $10.75 for 2.5 pounds of rib eye steak, so we have,
Substitute the values we have,
⇒ Price per pound = $10.75 / 2.5 pounds
Simplify the calculation, we get,
⇒ Price per pound = $4.30 per pound (rounded to the nearest cent)
Therefore, the price per pound of rib eye steak is $4.30.
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Martin works at a clothing store and earns commission off each item he sells. He earns 15% commission on each pair of shoes and 10% commission on each belt. Last week martin sold 3 pairs of shoes that each cost $53. 00 and 5 belts that each cost $15. 0. How much commission did he earn on these eights items
Martin's total commission is $23.85 + $7.50 = $31.35.
What is the percentage?
A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.
The total cost of the three pairs of shoes is $53.00 * 3 = $159.00
The total cost of the five belts is $15.00 * 5 = $75.00
Martin's commission on the shoes is 15% of $159.00 = $23.85
Martin's commission on the belts is 10% of $75.00 = $7.50
Therefore, Martin's total commission is $23.85 + $7.50 = $31.35.
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1 l is 1. 75 pints
1 gallon is 8 pint
what is the approximate number of gallons that are equal to 48000cm3
The approximate number of gallons that are equal to 48,000cm³ is
10.5 Gallons
How is this so?10.5 Gallons are equal to 48000 cm³ if 1 litre is approximately 1.75 pints, 1 gallon= 8 pints,
1000 cm³ = 1 Litre
48000 cm³ = 48 litre
1 litre is approximately 1.75 pints
=> 48 litre is approximately = 48 * 1.75 pints
= 84 Pints
8 pints = 1 Gallon
=> 1 pint = 1/8 Gallon
=> 84 Pints = 84/8 Gallons=
= 10.5 Gallons
So, 10.5 Gallons are equal to 48000 cm³
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The total amount I (in millions of dollars) of personal income earned in a state and the population P (in millions) of the state can be modeled by
1 =
6983t + 109,359
and P = 0. 0345t + 4. 909
0. 0059+ + 1
where t represents the number of years since 2000. Estimate the per capita income in 2022. (Per capita means per person. )
By dividing the state's total personal income of 268025 million dollars by its population of 5.5935 million, one can estimate the per capita income in 2022 to be around 47,917 dollars per person.
Finding the values of P and t for 2022 is necessary before we can determine the per capita income.
Assuming that t is the number of years since the year 2000, t will equal 22 in 2022.
The state's population in millions in 2022 can be determined using the P equation:
The P equation can be used to calculate the state's population in millions for the year 2022:
P = 0.034 (52) plus 4.909 to equal 5.5935 million
Using the computation for the total amount of personal income earned in the state, we can compute the total personal income in millions of dollars in 2022:
I is equal to 6983(22) + 109359, or 268025 trillion dollars.
To calculate the per capita income, we divide the total personal income by the population:
Total personal income divided by population yields a per-person income of 47,917 dollars (26,8025 / 5.5935).
Consequently, the amount of per capita income predicted for 2022 is almost 47,917 dollars per person.
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Which number line
3(8-4x)<6(x-5)
Answer:
3(8-4x)<6(x-5)
(24-12x)<(6x-30)
collect like terms
24+30<6x+12x
54 <18x
x<54/18
x<3
Therefore x is lesser than 3
Rewrite the exprossion in the form b^n b^1/5/b
The value of the expression is,
⇒ [tex]b^{- 4/5}[/tex]
We have to given that;
The expression is,
⇒ [tex]\frac{b^{1/5} }{b}[/tex]
Now, We can simplify the expression as;
⇒ [tex]\frac{b^{1/5} }{b}[/tex]
⇒ [tex]b^{\frac{1}{5}- 1 }[/tex]
⇒ [tex]b^{- 4/5}[/tex]
Thus, The value of the expression is,
⇒ [tex]b^{- 4/5}[/tex]
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The triangle shown is an equilateral triangle. What is the perimeter of the triangle?
Answer:
3
Step-by-step explanation:
Hey! Alright so since its equilateral all sides are congruent.
This means you can set these two equations equal to eachother:
5 - 2x = -4x + 9
2x = 4
x = 2
5 - 2(2) = 1
-4(2) + 9 = 1
Have a great day!!
keenan wants to make a paperweight at pottery class. he designs a pyramid-like model with a base area of 80 8080 square centimeters and a height of 7.5 7.57, point, 5 centimeters. the density of the clay he is using is 1.7 1.71, point, 7 grams per cubic centimeter. what is the weight of keenan's paperweight?
The weight of Keenan's paperweight is 340 grams using the volume of a pyramid given by V = (1/3)Bh.
To find the weight of Keenan's paperweight, we need to first find its volume. The volume of a pyramid is given by V = (1/3)Bh, where B is the area of the base and h is the height. Substituting the given values, we get:
V = (1/3)(80)(7.5) = 200 cm³
Next, we need to find the mass of the paperweight using the density of the clay. We know that density (p) is defined as mass (m) per unit volume (V), or p = m/V. Rearranging this equation, we get:
m = pV
Substituting the values, we get:
m = (1.7)(200) = 340 grams
Therefore, the weight of Keenan's paperweight is 340 grams.
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Jordan played three rounds of a video game. This table shows how many points he scored in each round.
How many points did he score in all?
1732 + 1273 + 1638 = 4643
this is the answer, hope it helps!
Solve x2 + 6x = 9 for x by completing the square. NEEEED HELP FAST
Step-by-step explanation:
Starting with x^2 + 6x = 9:
1. Move the constant term to the right side: x^2 + 6x - 9 = 0
2. Find the coefficient of x (which is 6) and divide it by 2: 6/2 = 3
3. Square the result from step 2: 3^2 = 9
4. Add the result from step 3 to both sides of the equation to complete the square: x^2 + 6x + 9 = 18
5. Factor the left side of the equation: (x + 3)^2 = 18
6. Take the square root of both sides of the equation: x + 3 = ±√18
7. Simplify the right side of the equation: x + 3 = ±3√2
8. Solve for x by subtracting 3 from both sides of the equation: x = -3 ±3√2
So the solutions are x = -3 + 3√2 and x = -3 - 3√2.
PLS mark my answer brainliest
Solving we get that option (C) that is x equals plus or minus root 18 minus 3 is correct.
What is Completing the Square?Completing the Square is a method used to solve a quadratic equation by changing the form of the equation so that the left side is a perfect square.
The steps of the method are as follows:
Isolate the number or variable c to the right side of the equation. Divide all terms by a (the coefficient of x2, unless x2 has no coefficient). Divide coefficient b by two and then square it. Add this value to both sides of the equation.
How to Solve x2 + 6x = 9 for x by completing the square?1). [tex]x^2+6x+\huge \text(\dfrac{6}{2} \huge \text)^2 =9+\huge \text(\dfrac{6}{2} \huge \text)^2[/tex]
2). [tex]\huge \text(x+\dfrac{6}{2} \huge \text)^2=18[/tex]
3). [tex](x+3)^2=18.[/tex]
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Complete Question-
Solve x2 + 6x = 9 for x by completing the square.
A. x = −6
B. x = 0
C. x equals plus or minus square root of 18 minus 3
D. x = x equals plus or minus square root of 18 plus 3
