To make an equation with fractions simpler we will be required to take up and LCM and cross-multiplication.
When an equation has fractions, there can be a case where each side, the LHS and the RHS, have multiple fractions with different denominators or even whole numbers.
In this case, first, you have to make sure to take an LCM for fractions on each side and make sure each side has only one denominator and all the constants and variables are a part of that fraction.
Then you have to take the denominator from each side and then multiply it with the numerator of the other. For example-
If an equation looks like [2x - 3]/5 = [4x + 8]/7
Here LHS has 5 as the denominator while RHS has 7
Hence, we will take 5 over to the RHS and 7 to LHS to get
7 X [2x - 3] = 5 X [4x + 8]
Now we have gotten our simpler form.
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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:
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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A coin of questionable fairness is tossed 10 times per set of trials for two sets of trials. the outcomes are ththththht and ttthtthtth (t = tails; h = heads). which model can you most likely rule out on the basis of this simulation?
The model that is most likely rule out on the basis of this simulation is 40%
What is probability?Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.
First set of trials: ththththht ( where T = Tails ; H = Heads)
Number of heads = 5
Number of outcomes = 10
Second set of trials: ttthtthtth
Number of heads = 3
Number of outcomes = 10
Total number of heads = 5 + 3 = 8
Total number of outcomes = 10 + 10 = 20
Probably of heads = 8/20 * 100%
Probably of heads = 0.4*100%
Probably of heads = 40%
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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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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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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]
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]
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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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?
5x - 6 = 44. what is x
Answer:
[tex]5x - 6 = 44 \\ \longrightarrow \: 5x = 44 + 6 \\ \longrightarrow \: 5x = 50 \\ dividing \: both \: sides \: by \: 5 \: \\ \\ \longrightarrow \: \cancel\frac{5x}{5} = \cancel\frac{50}{5} \\ \\ \longrightarrow \:\boxed{ x = 10}[/tex]
hope helpful! :)
Answer:
x = 10
Step-by-step explanation:
5x - 6 = 44. what is x
5x - 6 = 44
add 6 on both sides5x = 50
divide each side by 5x = 10
---------------------
check
5 x 10 - 6 = 44 (remember pemdas)
44 = 44
the answer is good
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.
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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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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The ratio of the ide length of Square A to the ide length of Square B i 4:9. The ide length of Square A i 12 yard. What i the area of Square B ?
Area of square B is 729.
Now, According to the question:
A square is a two-dimensional figure with four sides. It is also known as a quadrilateral. The area of a square is defined as the total number of unit squares in the shape of a square. In other words, it is defined as the space occupied by the square.
"Information available from the question"
We have been given that the ratio of the side length of square a to the side length of square b is 4:9. The side length of square a is 12 yards.
First of all, we will find the side length of square b using proportions as:
[tex]\frac{a}{b} = \frac{4}{9}[/tex]
[tex]\frac{12}{b}=\frac{4}{9}[/tex]
Cross multiplying the equation:
4b = 108
b = 108/4
b = 27
We know that area of a square is [tex]side^2[/tex]
=> b = 27
Area of square = [tex]27^2[/tex]
Area of square = 729
Hence, Area of square B is 729.
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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 %
write the equation with the least degree and integer coefficients that has the roots listed
3, 2 +-3i
The polynomial function is f(x) = (x - 3)((x - 2)² + 9)
How to determine the polynomial from the zeros?From the question, we have the following parameters that can be used in our computation:
Zeros: x=3, 2 +-3i
The polynomial can be repesented as
f(x) = product of (x - zeros)
using the above as a guide, we have the following:
f(x) = (x - 3)(x - (2 - 3i))(x - (2 + 3i))
This can be expressed as
f(x) = (x - 3)((x - 2)² + 9)
hence, the polynomial is f(x) = (x - 3)((x - 2)² + 9)
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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?
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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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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Write the equation for the linear function shown in the table
Answer:
y = 6x
Step-by-step explanation:
Each value of x is multiplied by 6 to get the corresponding y value
Write 8 3/4 as an improper fraction
Answer: 35/4
Step-by-step explanation:
8x4=32
32+3=35
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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coins are tossed. a. give an example of a simple event. b. give an example of a joint event. c. what is the complement of getting on the coin? d. what does the sample space consist of?
Coin tossing has a simple event of heads or tails, a joint event of multiple coin combinations, the complement of heads is tails, and sample space is {heads, tails}.
a. A simple event in coin tossing is getting either heads or tails on a single coin flip.
b. A joint event in coin tossing is getting heads on one coin and tails on another coin, for example.
c. The complement of getting heads on a coin flip is getting tails. The complement of getting tails is getting heads.
d. The sample space in coin tossing consists of all the possible outcomes of a single coin flip. This can be represented as a set, such as {heads, tails}. The sample space is the set of all possible outcomes of the experiment.
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Yvonne is using Triangle PQR with Altitude QS¯¯¯¯¯ shown below to prove the Pythagorean Theorem.
Given △PQR∼△QSR∼△PSQ, which conclusion about these triangles could Yvonne use in her proof of the Pythagorean Theorem?
Responses
PQQR=QSPS and QRPR=RSQR
P Q Q R = Q S P S and Q R P R = R S Q R
PQPR=PSPQ and QRPR=RSQS
P Q P R = P S P Q and Q R P R = R S Q S
PQPR=PSPQ and QRPR=RSQR
P Q P R = P S P Q and Q R P R = R S Q R
PQQR=QSSR and QSSR=PSQS
P Q Q R = Q S S R and Q S S R = P S Q S
The conclusions with regards to the similar right triangles, Yvonne needs to prove the Pythagorean Theorem are;
PQ/PR = PS/PQ and QR/PR = RS/QR
What is the Pythagorean Theorem?Pythagorean Theorem outlines the relationship between the length of the hypotenuse side and the lengths of the legs of a right triangle. The theorem states that the sum of the squares of the lengths of the legs of a right triangle, is equivalent to the square of the length of the hypotenuse side.
The specified similar triangles are;
ΔPQR ~ ΔQSR ~ ΔPSQ
PQ/PS = PR/PQ...(1)
(PQ)² = PS·PR
QR/RS = PR/QR...(2)
(QR)² = RS·PR
(PQ)² + (QR)² = PS·PR + PR/RS = PR·(PS + RS) = PR×PR = (PR)²
(PQ)² + (QR)² = (PR)²
Equations (1) and (2), can be expressed as follows;
PQ/PS = PR/PQ...(1)
Multiply both sides by PS/PR
PQ/PS × (PS/PR) = PR/PQ × (PS/PR)
PQ/PS × (PS/PR) = PQ/PR
PR/PQ × (PS/PR) = PS/PQ
Therefore;
PQ/PR = PS/PQQR/RS = PR/QR...(2)
Multiplying both sides by (SR/PR). we get;
QR/SR × (RS/PR) = QR/PR
PR/QR × (RS/PR) = RS/QR
QR/PR = RS/QRTherefore, the conclusions about the triangles, Yvonne can use in her proof of the Pythagorean Theorem are;
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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
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
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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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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