Translating the given sentence into a variable expression, we have:
2n - 5.
How can we explain it ?we have: n - (5 - n)
Simplifying the expression, we can use the distributive property and combine like terms:
n - 5 + n = 2n - 5
So the simplified expression is 2n - 5.
What is a variable ?A variable is a symbol or letter used to represent a value or set of values in a mathematical expression or equation. The value of a variable can change and can be determined by the problem or context. For example, in the equation y = 2x + 3, x is a variable that represents an unknown value, while y represents a related value that depends on the value of x. Variables are used to represent unknown or changing quantities and can be used to model real-world situations in mathematics.
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Write 8 3/4 as an improper fraction
Answer: 35/4
Step-by-step explanation:
8x4=32
32+3=35
Circumference: C = πrd or C = 2mr
Area: A= r² or A = π(r) (r)
REMEMBER: Each square box of the grid measures 1 unit (un) long and 1 unit (un) high!
What is the circumference of Circle G?
Use 3.14 for pl. Show your work here:
What is the area of Circle G? Use 3.14 for pl.
Show your work here:
Answer: 31.4
Step-by-step explanation: the circumference is 31.4 because the radius is 5, you multiply by 2 to get a diameter that is 10, then multiply that by 3.14 because in this question pi=3.14.
The price for gasoline is represented by the equation y = 2.72x, where y r represents the total price for x gallons of gasoline The graph goes through (5.44,2) and (8.16,3)
The graph goes through (5.44,2) and (8.16,3) is false.
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
Given that price for gasoline is represented by the equation y = 2.72x,
where y r represents the total price for x gallons of gasoline
We have to check whether the line passes through (5.44,2) and (8.16,3)
From the equation the slope is 2.72.
Now let us check whether the two points gives the same slope.
m=3-2/8.16-5.44
=1/2.72
=0.36
Hence, the graph goes through (5.44,2) and (8.16,3) is false.
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Two poles, 30 feet and 50 feet tall, are 40 feet apart and perpendicular to the ground. The poles are supported by wires
attached from the top of each pole to the bottom of the other, as in the figure. A coupling is placed at C where the two
wires cross.
Answer:
You provided plenty of background information, but please provide a question to be answered.
If A + B + C = π, express cos (A + B) in terms of angle C.
Answer:
te te te te te te te rog vreau să mă iai la un cont decent în privat de la școală dar trebuie să se poate mai bine tu nu mi-ai spus sa te sun se va întâmpla la un cont decent și a ride la un moment de la card memorie micro
Step-by-step explanation:
trebuie sa faci așa 4629+(703)-105
Answer:
cos(A + B) = - cosC
Step-by-step explanation:
using the addition identity
cos(x ± y) = cosxcosy ∓ sinxsiny
given
A + B + C = π ( subtract C from both sides )
A+ B = π - C
then
cos(A + B)
= cos(π - C)
= cosπ cosC + sinπ sinC
= - 1 × cosC + 0 × sinC
= - cosC + 0
= - cosC
How do you draw a bar model for "5y=95" "6b=12" "168/c=8" " v / 7=5"
will give full brainliest if someone shows me a demenstation pls help asap
The solution is given below.
What is Bar model?In maths a bar model is a pictorial representation of a problem or concept where bars or boxes are used to represent the known and unknown quantities. Bar models are most often used to solve number problems with the four operations – addition and subtraction, multiplication and division.
here, we have,
"5y=95"
"6b=12"
"168/c=8"
" v / 7=5"
so, the bar model ,
y = 95/5
=19
b= 12/6
= 2
c = 168/8
= 21
v = 5* 7
= 35
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5. Rachel used 5 ½ cups of sugar to make cherry cobbler. If each cobbler uses 1/3 cup of sugar, how many cobblers can she make?
Answer: 1 1/6
Step-by-step explanation:
use property 8 to estimate the value of the integral ∫1147xdx.
Using property 8 and the midpoint rule, we have estimated the value of the integral ∫1147xdx to be approximately 14.
Property 8 of the definite integral states that if a < b and 0 < c < d, then:
∫baf(x)dx = ∫dcf(x)dx - ∫caf(x)dx
We can use this property to estimate the value of the integral ∫1147xdx. Let's choose c = 1 and d = 4, so that 0 < c < d and a < b. Then:
∫1147xdx = ∫447xdx - ∫11x dx
Next, we can use a numerical method, such as the midpoint rule or trapezoidal rule, to estimate the value of each of the integrals on the right side of the equation.
For example, using the midpoint rule with n = 4 subintervals for each integral:
∫447xdx ≈ (4 - 4/2) + (4 - 3/2) + (4 - 2/2) + (4 - 1/2) = 4 + 4 + 4 + 4 = 16
∫11x dx ≈ (1 - 1/2) + (1 - 2/2) = 1 + 1 = 2
So, our estimate of ∫1147xdx becomes:
∫1147xdx ≈ 16 - 2 = 14
Therefore, using property 8 and the midpoint rule, we have estimated the value of the integral ∫1147xdx to be approximately 14.
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Write y=2/5x−2 in standard form.
Answer:
2x - 5y = 10
Step-by-step explanation:
the equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
given
y = [tex]\frac{2}{5}[/tex] x - 2 ( multiply through by 5 to clear the fraction )
5y = 2x - 10 ( subtract 2x from both sides )
- 2x + 5y = - 10 ( multiply through by - 1 )
2x - 5y = 10 ← in standard form
Which line of best fit tends to underestimate the bite force and would NOT make
good predictions on the relationship of body mass and bite force of crocodiles?
Sol's Line
Taylor's Line
Patti's Line
Marrisa's Line
Taylor's Line Best Fit does not accurately anticipate the relationship between crocodile body mass and bite force and has a tendency to overestimate the bite force.
An infinite sum of terms that are expressed in terms of the function's derivatives at a single point is the Taylor series, also known as the Taylor expansion, of a function. Near this point, the function and the sum of its Taylor series are equivalent for the majority of common functions.
What is the line's Taylor form?P1(x) = (a)+ f'(x a) The function close to x = an is best approximated linearly by the tangent line. The curve and tangent line have the same first derivative, or slope, at the point where x = a. This close estimate is a Taylor polynomial of degree 1 is referred to as P1 (x).
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Help pls just need to simplify
If angle b is two more than three times angle c, angle b and c are complimentary what is the measure of each angle
Step-by-step explanation:
"∠B is 2 more than 3 times the measure of ∠C" translates into B = 3C + 2....(1)
"...∠B and ∠C are complementary angles" translates to B + C = 90...............(2)
Now, all that's left to do is to solve for B and C. So, we'll take equation (1) and substitute it into equation (2) as follows:
(3C + 2) + C = 90
4C + 2 = 90
4C = 88
C = 22
Plugging C = 22 back into either equation (1) or (2) gives us
B = 90 - 22 = 68 (or B = 3(22) + 2 = 68)
Thus, ∠B = 68º; ∠C = 22º
PLEASE HEEEEEEEEEEEEEEEEEEEEEEEEEEEELP
Find the error in the following equations:
2. 4a ^ 2 * 3a ^ 5 = (4 + 3) * a ^ (2 + 5) = 7a ^ 7
3. x ^ 6 * x * x ^ 3 = x ^ (6 + 3) = x ^ 9
4. 3 ^ 4 * 2 ^ 3 = 6 ^ (4 + 3)
The errors in the equation is shown below.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 8 is an equation.
We have,
4a² x 3[tex]a^5[/tex]
= 4 x 3 x [tex]a^{2 + 5}[/tex]
= 12 [tex]a^7[/tex]
[tex]x^6[/tex] x (x) x x³
= [tex]x^{6 + 1 + 3}[/tex]
= [tex]x^{10}[/tex]
[tex]3^4[/tex] x 2³
= 3 x 3 x 3 x 3 x 2 x 2 x 2
= 81 x 8
= 648
Thus,
The equation is solved correctly above.
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Gabriella measured a line to be 11.1 inches long. If the actual length of the line is 11.6 inches, then what was the percent error of the measurement, to the nearest tenth of a percent
Answer:
10%
Step-by-step explanation:
11.6/11.1 = 0,1045045
There are 136 basketball fans who plan to go to a game. How many buses will be needed, given that each bus can hold 38 fans?
In baeball, each time a player get to hit the ball, it i recorded. The ratio of hit compared to total attempt i their batting average. Each player on the team want the to have the highet batting average to help their team the mot. So far Jana ha hit the ball 7 time out of 10 and Taha ha hit th ball 10 out of 16 time. Which player ga a ratio that mean they have a better batting average?
The player who has better batting average is Jenna
What are algebraic operations?They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
To solve this problem we must perform the following algebraic operations with the given information
Information about the problem:
Jenna = 7 times / 10 timeTasha = 10 times / 16 timesRatio = ?Calculating the ratio of both players we get:
Jenna ratio = 7/10
Jenna ratio = 0.7
Taha ratio = 10/16
Tasha ratio = 0.63
0.7 > 0.63
7/10 > 10/16
Jenna > Tasha
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Correctly written question:
In baseball each time a player get to hit the ball it is recorded. The ratio of hit compared to the total attempt is their batting average. Each player on the team wants to have the highest batting average to help their team the most. So far Jenna has hit the ball 7 times out a 10 and Tasha has hit the ball 10 out of 16 time. Which player has a ratio that mean they have a better batting average?
Let U and V be nxn orthogonal matrices. Explain why UV is an orthogonal matrix. [That is, explain why UV is invertible and its inverse is (UV)"]
Why is UV invertible?
A. Since U and V are nxn matrices, each is invertible by the definition of invertible matrices. The product of two invertible matrices is also invertible.
B. UV Is Invertible because it is an orthogonal matrix, and all orthogonal matrices are invertible.
C. Since U and V are orthogonal, each is invertible by the definition of orthogonal matrices. The product of two invertible matrices is also invertible.
D. UV is invertible because the product of any two matrices is always invertible
For the orthogonal matrices, the product of two invertible matrices is also invertible.
Orthogonal matrices are matrices that have a special property: the dot product of each of their rows or columns is equal to 0.
The dot product of two vectors is equal to 0 when the vectors are orthogonal to each other, meaning they are perpendicular.
Since U and V are orthogonal matrices, each is invertible by the definition of orthogonal matrices.
The inverse of an orthogonal matrix is its transpose.
This is because the dot product of each row (or column) with itself is equal to 1, so the transpose of an orthogonal matrix is its inverse.
The product of two invertible matrices is also invertible, so UV is invertible.
Answer C is correct.
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Please help quick help
The perimeter of the actual triangle is 74 and option D is the correct answer.
What is scale factor?The scale factor is the difference in size between the original item's scale and that of the new object, which is a representation of it (bigger or smaller).
Given that the scaled dimension of the triangular face has the following dimensions:
PQ = 12
QR = PQ(1 + 25/100) = 12(125/100) = 15
PR = 2/3 (QR) = 2/3 (15) = 10
The scaling factor is 1/2 hence the actual dimensions of the triangle would be:
Original segments (1/2) = Scaled segment
Scaled (2) = Original
Using the above we have:
PQ = (12)(2) = 24
QR = (15)(2) = 30
PR =(10) (2) = 20
The perimeter of the triangle is the sum of all it sides:
P = 24 + 30 + 20
P = 74
The perimeter of the actual triangle is 74 and option D is the correct answer.
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suppose he starts with the same square of card, but changed the 4 inches to a different measurement. what is the largest volume he can make the box
The volume of the box will be 3136 cu. inches and the largest volume the box can be made of is also the same.
The amount of space occupied by a three-dimensional object as measured in cubic units.
The given square after getting folded turns into a box of 28*28*4 inches. The volume of the box can be determined by using the formula of volume of the cuboid.
Volume of the cuboid = 28*28*4
Volume of the cuboid =3136 cu. inches
The largest volume that the box can have is 3136 cu. inches as when increasing the height, the length or the width will decrease and so does the volume.
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You want the banner you are creating form one piece of cloth to be a golden rectangle. The clothe will be cut from a bolt that is 54 in wide. What are the dimensions
of the largest banner that you can make? Golden Ratio 1.618/1
54 in by
The dimensions of the largest banner are 54 inches by 87.372 inches.
What is a golden rectangle?A dividable rectangle is referred to as a "golden rectangle." into shapes that are similar to the original square and rectangle. Repeated golden rectangles form a pattern. displayed to the right. Each produced golden rectangle is duplicated and divided once more. All of the golden rectangles are like the original rectangle in shape.
Given a golden rectangle,
width of rectangle = 54 inch
let length be l,
according to the golden ratio,
l/b = 1.618/1
l = 1.618b
l = 1.618*54
l = 87.372 inches
Hence the dimensions are 54 inches by 87.372 inches.
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in town A , the population increased from 2000 to 2400 in 2 years. In town B, the population increased from 1800 to 2300 during the same time period. In which town is the percentage increase in population greater?
Answer: Town B
Step-by-step explanation:
Town A -
2400 - 2000 = 400
percentage increase = 400/2000x100
= 20 %
Town B -
2300 - 1800 = 500
percentage increase = 500/1800x100
= 27. 78 %
I really need help with this question please and thank you
Answer:
8.5
Step-by-step explanation:
this is a right triangle so we could use the formula, which is Pythagorean theorem
so it is [tex]13.5^{2} -10.5^{2} =72\\\sqrt{72} =8.5[/tex]
A drone is flying at the altitude of 16 1/4 feet above sea level a groundhog is directly below the drone at an altitude of 7 3/8 feet below sea level what is the distance between the drone and the groundhog
one is above sea level the other below sea level, so their distance is just their sum from sea level, so hmmm let's convert the mixed fractions to improper fractions and then sum them up.
[tex]\stackrel{mixed}{16\frac{1}{4}}\implies \cfrac{16\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{65}{4}} ~\hfill \stackrel{mixed}{7\frac{3}{8}} \implies \cfrac{7\cdot 8+3}{8} \implies \stackrel{improper}{\cfrac{59}{8}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{65}{4}+\cfrac{59}{8}\implies \cfrac{(2)65~~ + ~~(1)59}{\underset{\textit{using this LCD}}{8}}\implies \cfrac{130+59}{8}\implies \cfrac{189}{8}\implies 23\frac{5}{8}[/tex]
y=2x and -6x + 3y = 16
Answer:
0 [tex]\neq[/tex] 16
two equations have no solution and if you graphed them their lines would not intersect, they would be parallel
Step-by-step explanation:
we can substitute the value of 'y' which is '2x' into the second equation as follows:
-6x + 3(2x) = 16
-6x + 6x = 16
0 [tex]\neq[/tex] 16
therefore, these two equations have no solution and if you graphed them their lines would not intersect, they would be parallel
Are -20 degrees and 340 degrees co-terminal angles? Why? Show your work to earn full credit.
Yes -20 degrees and 340 degrees are co-terminal angles
What are co-terminal angles?are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side. For example, the angles 30°, –330°.
The coterminal angles can be positive or negative. To find the coterminal angles, simply add or subtract 360 degrees as many times as needed from the reference angle. All of these angles are coterminal angles.
co-terminal angles are found by adding or subtracting 360° to the angles.
for example the co-terminal angles of -10° = -10° + 360 = 350°
Similarly The co-terminal angles of -20 = -20+360 = 340°
therefore the -20 and 340 are co-terminal angles
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you are choosing between two health clubs. Club A offers membership for a fee of $21 plus a monthly fee of $22. Club B offers membership for a fee of $12 plus a monthly fee of $25. After how many months will the total cost of each health club be the same? What will be the total cost for each club?
After the second month, the charge will remain the same. 14 + 28 (2) = $70 would be the final price.
How to find the calculation?The first club offers a lower membership cost but a higher monthly fee in this instance, while the second club offers the polar opposite.
The computation would then be as follows to determine how long it would take for the total cost of each health club to equalize:
Example:
1 club fee equals 2 clubs fees
14+ 28x= 24+ 23x
28x-23x= 24-14
5x= 10 \sx=2
After the second month, the charge will remain the same. 14 + 28 (2) = $70 would be the final price.
The Complete Question.
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consider a function with three variables: a, b, c. convert to sum-of-minterms form:
The sum-of-minterms form of the function f(a,b,c) = a'b + ac is (a'b + ac).
To convert a function with three variables to sum-of-minterms form, we first need to determine the truth table of the function, which lists all possible combinations of inputs and the corresponding outputs. Then, we identify the minterms (i.e., combinations of inputs that result in a 1 output) and represent each minterm as a binary number. The sum-of-minterms form of the function is then the sum of all the binary numbers representing the minterms.
For example, consider the function f(a,b,c) = a'b + ac. (The truth table for this function is attached below)
From the truth table, we can see that the minterms are (0,1,1) and (1,0,1), which can be represented as binary numbers 011 and 101, respectively. The sum-of-minterms form of the function is then:
f(a,b,c) = 011 + 101 = (a'b + ac)
So, the sum-of-minterms form of the function f(a,b,c) = a'b + ac is (a'b + ac).
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distinct vertices of an octagon are chosen at random. what is the probability that they are adjacent?
If distinct vertices of an octagon are chosen at random , then the probability that they are adjacent is 2/7 .
An Octagon has 8 vertices, so there are 8 possible vertices to choose from. To find the probability that two chosen vertices are adjacent, we need to determine the number of ways in which two adjacent vertices can be chosen,
Since there are 8 vertices and each vertex has 2 adjacent vertices,
The total number of pairs of vertices in octagon is = ⁸C₂ = 28;
the possible Adjacent pairs are : {(1,8),(1,2),(2,3),(3,4),(4,5),(5,6),(6,7),(7,8)} ;
So , probability of vertices being adjacent is = 8/28 ;
Simplifying further , we get ;
Probability ⇒ 2/7 .
Therefore , the probability that vertices are adjacent is 2/7 .
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need the answers for all pls
From the given table it is visible that the value of s(5)=4.2
What is value function?When the variables and constants in a mathematical expression are given values, the outcome of the computation it describes is the expression's value. The amount that the function assumes for these argument values is the value of a function, given the value(s) assigned to its argument(s).
functions with return values and arguments. Functions with arguments and no return values.... This function takes arguments and returns a value.
functions with return values and no arguments.
without return values and without arguments
Function value can mean: The result of applying a function to an argument in mathematics. a closure in computer science.
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if 0≤b≤2, for what value of b is ∫b0cos(ex)dx a minimum?
The value of b for which ∫b0cos(ex)dx is minimum is π/2e..
To find the value of b for which the definite integral ∫b0cos(ex)dx is a minimum, we can find the critical points (i.e. local extrema) of the integrand cos(ex) in the interval [0, 2].
Since cos(ex) is a periodic function with period 2π/e, it suffices to consider the interval [0, 2π/e]. In this interval, cos(ex) has its maximum value of 1 at x = 0, and its minimum value of -1 at x = π/2e and x = 3π/2e.
Since e is positive, the function cos(ex) is increasing on the interval [0, π/2e) and decreasing on the interval (π/2e, π/e].
Therefore, if b is in the interval [0, π/2e), the integral is minimized when b = 0. If b is in the interval [π/2e, π/e], the integral is minimized when b = π/2e.
Since the maximum value of b is 2, and 2 < π/e, it follows that the integral ∫b0cos(ex)dx is minimized when b = π/2e.
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