The three equivalent equations are 2 + x = 5, x + 1 = 4 and -5 + x = -2. So, correct options are A, B and E.
Two equations are considered equivalent if they have the same solution set. In other words, if we solve both equations, we should get the same value for the variable.
To determine which of the given equations are equivalent, we need to solve them for x and see if they have the same solution.
Let's start with the first equation:
2 + x = 5
Subtract 2 from both sides:
x = 3
Now let's move on to the second equation:
x + 1 = 4
Subtract 1 from both sides:
x = 3
Notice that we got the same value of x for both equations, so they are equivalent.
Next, let's look at the third equation:
9 + x = 6
Subtract 9 from both sides:
x = -3
Since this value of x is different from the previous two equations, we can conclude that it is not equivalent to them.
Now, let's move on to the fourth equation:
x + (-4) = 7
Add 4 to both sides:
x = 11
This value of x is also different from the first two equations, so it is not equivalent to them.
Finally, let's look at the fifth equation:
-5 + x = -2
Add 5 to both sides:
x = 3
Notice that we got the same value of x as the first two equations, so this equation is also equivalent to them.
So, correct options are A, B and E.
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Complete question is:
Which of the following equations are equivalent? Select three options.
2 + x = 5
x + 1 = 4
9 + x = 6
x + (- 4) = 7
- 5 + x = - 2
Solve for b
Y=1/3x+b
Answer:
(3xy - 1)/3x = b
Step-by-step explanation:
make b the subject of formula
then simply it
did you get it
Answer:
b=Y-x/3
Step-by-step explanation:
Solve for b by simplifying both sides of the equation, then isolating the variable.
have a great day and thx for your inquiry :)
2
Select the correct answer from the drop-down menu.
Which equation satisfies all three pairs of a and b values listed in the table?
a b
0-10
1 -7
2-4
The equation is
An equation that satisfies all three pairs of a and b values listed in the table include the following: C. 3a - b = 10.
How to determine an equation that satisfies all three pairs of a and b values listed in the table?In order to determine an equation that satisfies all three pairs of a and b values listed in the table, we would substitute each of the numerical values corresponding to each variable into the given equations and then evaluate as follows;
a - 3b = 10
0 - 3(-10) = 30 (False).
3a + b = 10
3(0) - 10 = -10 (False).
3a - b = 10
3(0) - (-10)
0 + 10 = 10 (True).
3a - b = 10
3(1) - (-7)
3 + 7 = 10 (True).
3a - b = 10
3(2) - (-4)
6 + 4 = 10 (True)
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Complete Question:
Which equation satisfies all three pairs of a and b values listed in the table?
a b
0 -10
1 -7
2 -4
The equation is?
A.) a-3b=10
B.) 3a+b=10
C.) 3a-b=10
D.) a+3b=10
Maurice ran 110 meters in 20.9 seconds. Yolanda ran 110 meters in 20.0 seconds. Who had the fastest time, Maurice or Yolanda?
A.Yolanda
B.Maurice
apex
Answer: I believe the answer is Yolanda.
Step-by-step explanation: Because Maurice ran 110 meters in 20.9 seconds, which is slower than Yolanda. Completing the race in 20 seconds is better than 20.9 seconds.
A sequence can be generated by using an= 3an-1, where a1 = 10 and n is a whole number greater than 1.
What are the first 3 terms in the sequence?
A. 3, 13, 23
B. 10, 30, 90
C. 10, 13, 16
D. 3, 30, 300
Answer:
B
Step-by-step explanation:
using the recursive rule [tex]a_{n}[/tex] = 3[tex]a_{n-1}[/tex] and a₁ = 10, then
a₁ = 10
a₂ = 3a₁ = 3 × 10 = 30
a₃ = 3a₂ = 3 × 30 = 90
the first 3 terms are 10 , 30 , 90
The cosine of θ is −0.95. What is sin(θ)?
The value of sin(θ) is 0.31 and it lies in the third and fourth quadrants. if the value of the cosine of θ is −0.95.
cos(θ) = -0.95
To calculate the value of sin(θ), we can use the Pythagorean theorem:
[tex]sin^{2}[/tex] (θ) +[tex]cos^{2}[/tex] (θ) = 1
We can rearrange the Pythagorean identity to solve for sin(θ):
[tex]sin^{2}[/tex] (θ)= 1 - [tex]cos^{2}[/tex]
sin(θ) = ±[tex]\sqrt{1-cos^{2}}[/tex] *(θ)--------- (equation 1)
Substitute the value of the cosine of θ = −0.95 in Equation 1
sin(θ) = ±[tex]\sqrt{1-cos^{2}}[/tex] *(θ)
sin(θ) = ±[tex]\sqrt{(1 - 0.9025)}[/tex]
sin(θ) = ±[tex]\sqrt{0.0975}[/tex]
The positive value determines that the value is in the first and second quadrants, Negative shows the third and fourth quadrants.
sin(θ) = [tex]\sqrt{ 0.0975}[/tex]
sin(θ) = 0.312
Therefore, we can conclude that the value of sin(θ) is 0.312.
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Find g(0), g(-1), g(2), and g(2/3)
for g(x) =x/ square root 1-x^2
Given statement solution is :- Outputs and values g(2/3) = 2/3.
To summarize:
g(0) = 0
g(-1) = undefined
g(2) = undefined
g(2/3) = 2/3
To find the values of g(x) for the given inputs, we substitute each input into the function g(x) = x / √([tex]1 - x^2[/tex]). Let's calculate the values:
g(0):
Substitute x = 0 into the function:
g(0) = 0 / √([tex]1 - 0^2[/tex])
= 0 / √(1 - 0)
= 0 / √1
= 0
Therefore, g(0) = 0.
g(-1):
Substitute x = -1 into the function:
g(-1) = (-1) / √(1 - [tex](-1)^2[/tex])
= (-1) / √(1 - 1)
= (-1) / √0
Since the square root of 0 is undefined, g(-1) is undefined.
g(2):
Substitute x = 2 into the function:
g(2) = 2 / √([tex]1 - 2^2[/tex])
= 2 / √(1 - 4)
= 2 / √(-3)
Since the square root of a negative number is undefined in the real number system, g(2) is undefined.
g(2/3):
Substitute x = 2/3 into the function:
g(2/3) = (2/3) / √(1 - [tex](2/3)^2[/tex])
= (2/3) / √(1 - 4/9)
= (2/3) / √(5/9)
= (2/3) / (√5/√9)
= (2/3) / (√5/3)
= (2/3) * (3/√5)
= 2√5 / 3√5
= 2/3
Therefore, outputs and values g(2/3) = 2/3.
To summarize:
g(0) = 0
g(-1) = undefined
g(2) = undefined
g(2/3) = 2/3
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2. Convert the following into a single log statement from the many log statements to 1.
2 Log w+ log 7-3 log x-8 log y
NOTE: You must show this in at least two steps.
1st line should be to convert the 2 the 3 and the 8 only.
2nd line can be the final answer.
A single log statement from the many log statements to 1 is: [tex]log(7wy^{(-8)}/x^3)[/tex]
The exponent that indicates the power to which a base number is raised to produce a given number are called logarithm.
Use the logarithmic identity:
log[tex](a^n)[/tex] = n*log(a)
to convert the coefficients 2, 3, and 8:
log w + log 7 - 3log x - 8log y
= log w + log 7 - log [tex]x^3[/tex] - log [tex]y^8[/tex]
Combine the terms on the right-hand side using the logarithmic identity:
log(a) + log(b) = log(ab)
log w + log 7 - log[tex]x^3[/tex] - log [tex]y^8[/tex]
= log([tex]7wy^{-8}/x^3[/tex])
Therefore, the single log statement is from the many log statements to 1 is: log[tex](7wy^{-8}/x^3)[/tex]
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Kenya wants to open a savings account at a bank. The bank offers a savings account that pays
out 8% annual interest. If Kenya wants at least $7,000 in his account after 15 years, how much does
Kenya need to put in the account initially?
Kenya needs to initially put in the amount of $2,208.2in the account to have at least $7,000 after 15 years.
We can use the formula for compound interest:
A = P(1 + r/n)ⁿ
where A is the amount of money in the account after t years, P is the initial principal, r is the annual interest rate (as a decimal), and n is the number of times per year the interest is compounded.
Here, we want to find P, so we can rearrange the formula as:
P = A / (1 + r/n)ⁿ
We are given that r = 0.08 (8% interest) and n = 1 (interest is compounded annually).
We also know that A = $7,000 and t = 15 years.
So we can plug in these values and solve for P:
P = 7000 / (1 + 0.08/1)¹⁵
P = 7000 / (1.08)¹⁵
P ≈ $2,208.2
Therefore, Kenya needs to initially put in approximately $2,208.2in the account to have at least $7,000 after 15 years.
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Round 73,609 to the nearest thousand
Answer:
74,000
Step-by-step explanation:
use intelligence
find the center and radius by completing the square x2+6x+y2-4y=3
Answer:
Center: (-3, 2)
Radius: 4
Step-by-step explanation:
x2 + 6x + y2 - 4y = 3
x² + 6x + 9 + y² - 4y + 4 = 3 + 9 + 4
(x + 3)² + (y - 2)² = 16
(x + 3)² + (y - 2)² = 4²
Center: (-3, 2)
Radius: 4
A square has an area of 56 units, find the length of the side in simplest form. Has to be an Improper fraction.
The length of the side of the square in simplest form is 2sqrt(14).
The area of a square is given by the formula [tex]A = s^2[/tex], where A is the area and s is the length of a side.
We are given that the area of the square is 56 units, so we can set up the equation:
[tex]56 = s^2[/tex]
To solve for s, we can take the square root of both sides of the equation:
sqrt(56) = [tex]sqrt(s^2)[/tex]
We can simplify the square root of 56 by factoring it:
sqrt(56) = sqrt(222*7) = 2sqrt(14)
So, we have:
2sqrt(14) = s
This is an improper fraction because the numerator is larger than the denominator. Therefore, the length of the side of the square in simplest form is 2sqrt(14).
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For positive acute angles A and B, it is known that SinA= 11/61 and tan B=4/3. Find the value of Cos(A-B) in simplest form.
For positive acute angles A and B, if it is known that SinA= 11/61 and tan B=4/3, cos(A-B) = 224/305.
We can use the trigonometric identity cos(A-B) = cosA cosB + sinA sinB to find the value of cos(A-B).
First, we need to find the value of cosA and sinB:
Since sinA = opposite/hypotenuse, we can draw a right triangle with opposite side 11 and hypotenuse 61, and use the Pythagorean theorem to find the adjacent side:
cosA = adjacent/hypotenuse = √(61² - 11²)/61 = 60/61
Since tanB = opposite/adjacent, we can draw another right triangle with opposite side 4 and adjacent side 3, and use the Pythagorean theorem to find the hypotenuse:
hypotenuse = √(4² + 3²) = 5
sinB = opposite/hypotenuse = 4/5
Now we can substitute these values into the formula:
cos(A-B) = cosA cosB + sinA sinB
= (60/61)(3/5) + (11/61)(4/5)
= 180/305 + 44/305
= 224/305
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Find (if possible) a. AB and b. BA.
A=
-
2
-
8
B=
||||
6
S
3
2
The products of the matrices A and B are [tex]AB = \left[\begin{array}{cc}-50 &7\\44 &-10\end{array}\right][/tex] and [tex]BA = \left[\begin{array}{cc}-12&-24 \\-16&-48\end{array}\right][/tex]
Finding the products of the matrices A and BFrom the question, we have the following parameters that can be used in our computation:
Matrix A = [tex]\left[\begin{array}{cc}-3&-8\\2&8\end{array}\right][/tex]
Matrix B = [tex]\left[\begin{array}{cc}6&3\\4&-2\end{array}\right][/tex]
Using the above as a guide, we have the following:
[tex]AB = \left[\begin{array}{cc}-3 * 6 + -8 * 4 &-3 * 3 -8 * -2\\2 * 6 + 8 * 4 &2 * 3 + 8 * -2\end{array}\right][/tex]
Evaluate
[tex]AB = \left[\begin{array}{cc}-50 &7\\44 &-10\end{array}\right][/tex]
Next, we have
[tex]BA = \left[\begin{array}{cc}6 * -3 + 3 * 2&6 * -8 + 3 * 8 \\4 * -3 + -2 * 2&4 * -8 + -2 * 8\end{array}\right][/tex]
Evaluate
[tex]BA = \left[\begin{array}{cc}-12&-24 \\-16&-48\end{array}\right][/tex]
Hence, the values are [tex]AB = \left[\begin{array}{cc}-50 &7\\44 &-10\end{array}\right][/tex] and [tex]BA = \left[\begin{array}{cc}-12&-24 \\-16&-48\end{array}\right][/tex]
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MA.7.AR.4.1
Johnny and Eleanor went to their local gas station to collect information about the cost of
fuel for compact cars. They observed both regular and premium gas purchases that day and
recorded their data in the table below.
Gallons Purchased 11.5 7.2
10
14.3 6.8
9.7
Cost
$25.23 $15.80 $21.94 $40.63 $14.92 $27.56
Part A. Is there a proportional relationship between the number of gallons of gas sold and
the cost? Explain your answer.
Part B. If the relationship is not proportional, which data value or values should be
changed to make the relationship proportional? What could explain this
difference?
a) The fourth and sixth data points have significantly different ratios.
a) Let's calculate the ratios:
For the first data point:
= 11.5 gallons / $25.23 = 0.4555 gallons per dollar
For the second data point:
= 7.2 gallons / $15.80 = 0.4557 gallons per dollar
For the third data point:
= 10 gallons / $21.94 = 0.4556 gallons per dollar
For the fourth data point:
= 14.3 gallons / $40.63 = 0.3519 gallons per dollar
For the fifth data point:
= 6.8 gallons / $14.92 = 0.4555 gallons per dollar
For the sixth data point:
= 9.7 gallons / $27.56 = 0.3517 gallons per dollar
However, the fourth and sixth data points have significantly different ratios.
b) If the relationship is not proportional, the data values that should be changed to make the relationship proportional are the fourth and sixth data points.
The difference in ratios could be explained by factors such as fluctuations in gas prices or differences in gas grades.
To establish a proportional relationship, it would be necessary to collect data where the price per gallon remains constant for all data points or to separate the data based on gas grades and analyze each grade separately.
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what do you add to get the pattern 1, 8, 15, 22, 29 36, 43
Answer:
7
Step-by-step explanation:
Finding the common difference of an arithmetic sequence is easy peasy lemon squeezy. All you have to do is take any term and subtract it from the next one. For instance, if you take 1 and subtract it from 8, you get 7. If you take 8 and subtract it from 15, you get 7 again. You can do this for any pair of terms and you will always get 7. That's the common difference of the sequence 1, 8, 15, 22, 29, 36, 43. It means that you just add 7 to each term to get the next one. Isn't that neat?
The sum of Jerry's and Carrie's ages is 52. Jerry is 4 years older than Carrie. What is Jerry's age?
Answer:
28
Step-by-step explanation:
let's assumed that
x = Jerry's age
y = Carrie's age
if Jerry 4 years older that Carrie
x = y + 4
x + y = 52
(y + 4) + y = 52
2y + 4 = 52
2y = 48
y = 24
x = y + 4
x = 24 + 4
x = 28
#CMIIWThe bottom part says how many student tickets where brought? Can anyone pls help me PLSS
255 number of adults and 355 number of students bought ticket.
Here, we have,
Let the number of adults bought tickets are x and the number of students that bought tickets is (x + 100).
Since it is given that 100 more students brought tickets than adults.
Now, each adult ticket costs $5 and each student's ticket costs $3.5 and the total collected value of tickets is $2517.5.
So, 5x + 3.5(x + 100) = 2517.5
⇒ 8.5x + 350 = 2517.5
⇒ 8.5x = 2167.5
⇒ x = 255
So, 255 number of adults and (255 + 100) = 355 number of students bought ticket. (Answer)
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What are the solutions to the system of equations graphed?
Answer:
(- 2, 0 ) , (1, - 3 )
Step-by-step explanation:
the solutions to the system of equations are at the points of intersection with the curve and the straight line.
points of intersection are at (- 2, 0 ) and (1, - 3 ) , then
solutions are (- 2, 0 ) , (1, - 3 )
18. Multiply, then check your work by switching factors.
a. 693 x 83
b. 910 x 45
c. 38 x 84
d. 409 x 89
The requried, Multiplies(with switching factors.) area given below,
a.
693 x 83 = 57489
83 x 693 = 57489
The answer is 57489.
b.
910 x 45 = 40950
45 x 910 = 40950
The answer is 40950.
c.
38 x 84 = 3192
84 x 38 = 3192
The answer is 3192.
d.
409 x 89 = 36401
89 x 409 = 36401
The answer is 36401.
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What is the total cost of 20 books at R25 each?
Answer:
R500
Step-by-step explanation:
20 books x R25 each = R500.
Darlene purchases $20,000 worth of stock on her brokers advice and pays her broker a 1.5% broker fee
Darlene's net proceeds from the investment into shares would be $ 8, 279 .
How to find the net proceeds ?First, find the initial broker fee:
= Initial investment × Broker fee rate
= 20, 000 x 1. 5 %
= 20, 000 x 0. 15
= $ 300
The total fees incurred to buy and sell are:
= 300 initial broker + 21 later broker
= $ 321
The net proceeds would then be:
= Final value of stock - Initial investment - Total fees
= 28, 600 - 20, 000 - 321
= 8, 600 - 321
= $ 8, 279
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Full question is:
Darlene purchases $20,000 worth of stock on her brokers advice and pays her broker a 1.5% broker fee. She sells her stock when it increases to $ 28,600 two years later, and uses a discount broker who charges $21 per trade. Compute Darlene's net proceeds after the broker fees are taken out.
4. Approximate the solution to this system of equations.
y = -2x+6
y = 4x - 1
The solution of the system of linear equations, is (1.167, 3.667).
Given that the system of linear equations, y = -2x+6 and y = 4x - 1, we need to find the solution for the same,
y = -2x+6............(i)
y = 4x - 1.......(ii)
Equating the equations since the LHS is same,
-2x+6 = 4x-1
6x = 7
x = 1.167
Put x = 1.16 to find the value of y,
y = 4(1.16)-1
y = 4.66-1
y = 3.667
Therefore, the solution of the system of linear equations, is (1.167, 3.667).
You can also find the solution using the graphical method,
Plot the equations in the graph, the point of the intersection of both the lines will be the solution of the system of linear equations, [attached]
Hence, the solution of the system of linear equations, is (1.167, 3.667).
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Please help me answer this question ASAP!! It’s due tomorrow! Will mark as brainliest if explained very simply and correct.
Answer:
The answer is B:14
Step-by-step explanation:
When you simply multiply 5% by 14, you get 0.7. So you know that 5% of 14 is 7.
Find surface area without mistaking the lateral height.
The total "surface-area" of cone having "slant-height" as 10, and base-radius as 6, is 301.44 square units.
The total surface area of a cone can be calculated by adding the area of the base to the lateral surface area.
Let us first calculate the lateral surface area of the cone:
Lateral surface area = πrl; where r is radius , and 'l" = slant-height,
The radius of base = 6 units and slant height is = 10 units.
So, we have:
Lateral surface area = π × 6 × 10
Lateral surface area = 60π square units
Next, Area of the base = πr²;
Area of the base = π × 6²,
Area of the base = 36π square units,
Total surface area = Lateral surface area + Area of the base
Total surface area = 60π + 36π
Total surface area = 96×3.14 = 301.44 square units.
Therefore, the total surface area of cone is 301.44 square units.
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How do I divide this somebody please help
Answer:
3
Step-by-step explanation:
factorize whats common in the question
division turns to multiplication by Inverwing the fraction
at the end of the day you will be left with 3
I hope you understand
The domain of this emath equation is
Answer:
x ≥ 5
Step-by-step explanation:
You want the domain of the equation y = √(x -5) -1.
DomainThe domain of the function is the set of x-values for which it is defined. The square root is not defined for negative values, so the domain is ...
x -5 ≥ 0
x ≥ 5 . . . . . . the domain of this function
__
Additional comment
The range is the set of y-values the function may produce. Here, that set of values is y ≥ -1.
<95141404393>
The Nut Shack sells cashews for $6.80 per pound and Brazil nuts for $4.70 per pound. How much of
each type should be used to make a 37 pound mixture that sells for $5.78 per pound?
Round answers to the nearest pound.
pounds of cashews
pounds of Brazil nuts
> Next Question
Answer:
Step-by-step explanation:
$6.80 x 19 pounds = $129.2
$4.70 x 18 pounds = $84.6
+___________________
37 pounds = $213.8
$213.8 divided by 37 pounds = 5.77837......
= $5.78 per pound
Please help me understand this problem!
The requried solution of the given derivative has been given below.
If F(t) is an antiderivative of t⁵, then we have:
F'(t) = d/dt(F(t)) = t⁵
According to the Second Fundamental Theorem of Calculus, we have:
[tex]\int_1^x t^5 dt = F(x) - F(1)[/tex]
Using this formula, we can find [tex]d/dx(\int_1^x t^5 dt)[/tex] as follows:
[tex]d/dx(\int_1^x t^5 dt) = d/dx(F(x) - F(1)) = F'(x) - 0 = t^5[/tex]
Therefore, [tex]d/dx(\int_1^x t^5 dt) = t^5.[/tex]
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Remove the parentheses from the following expression, and combine like terms: 4(ab²+1/₂c + x) - 2(c+x) A. 4ab² + 2x B. 4ab2 + 2x + C C. 4+abc2 + 2x D. 2ab²+2c + X
Answer:
A. 4ab² + 2x
Step-by-step explanation:
If you want to get rid of those pesky parentheses, you have to use the superpower of distributive property. It lets you multiply everything inside the parentheses by the number outside. For example:
4(ab²+1/₂c + x) = 4ab² + 2c + 4x
Boom! No more parentheses!
To combine like terms, you have to add or subtract the numbers in front of the terms that have the same variable and exponent. For example:
2x - 4x = -2x
Bam! Only one x left!
Here are the steps to simplify the expression:
4(ab²+1/₂c + x) - 2(c+x)
= 4ab² + 2c + 4x - 2c - 2x (use superpower)
= 4ab² + 4x - 2x (combine like terms)
= 4ab² + 2x (simplify)
So, the answer is A. 4ab² + 2x.
what is the probability of spinning a blue, then green
The probability of getting Blue then Green while spinning the wheel is
3 / 32
Probability is a branch of mathematics that helps us to understand the likelihood of an event occurring. It is represented by a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain. Probability can be used to make predictions and informed decisions in real-world situations.
From the given figure we can find out the following information
The probability of getting Blue While spinning the wheel = 3/8
The probability of getting Green While spinning the Wheel = 2 / 8
The probability of getting Blue then Green while spinning the wheel
= 3/8 * 2/8
= 6/64
= 3/32
Therefore, probability of getting Blue then Green while spinning the wheel is 3 / 32
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