Final answer:
After solving the original equation 2/3(6x+12)=-24, we find x = -8. Comparing this solution with the provided equations, the ones that have the same value for x are 9x+18=-24, 18x+36/2=-24, and x=-8.
Explanation:
To find which equations have the same value for x as 2/3(6x+12)=-24, we must first solve the original equation to find the value of x it yields:
2/3(6x+12) = -24
Multiply both sides by 3/2 to eliminate the fraction:
6x + 12 = -24 * (3/2)
6x + 12 = -36
Subtract 12 from both sides:
6x = -48
Divide by 6:
x = -8
Now we will compare this solution with the other equations:
4x+8=24 -> Does not match.9x+18=-24 -> When solving for x, we get x=-8, which matches.4x+12=-24 -> Does not match.18x+36/2=-24 -> Simplify to get 9x+18=-24, x = -8, matches.4x=-36 -> Does not match.4x=-32 -> Does not match.x=-9 -> Does not match.x=-8 -> Directly given the solution, which matches.Therefore, the equations that have the same value of x as the original equation are 9x+18=-24, 18x+36/2=-24, and x=-8.
How is angle a related to angle d?
A) vertical angles
B) alternate interior angles
C) alternate exterior angles
D) corresponding angles
Answer: Option 'A' is correct.
Step-by-step explanation:
since we have given a line AB and CD such that AB║CD,
And a transversal say 'l' cut the two parallel lines
And we know that when a transversal cuts two parallel lines we get linear pair and corresponding angles
But relation between angle 'a' and angle 'd' is vertically opposite angles.
So, Option 'A' is correct.
Which is an example of a function?
the time it takes to mow a lawn and the age of the person mowing the lawn
the distance to school and the time you spend at school
the price of a movie ticket and the height of the customer
the price of a piece of cloth and the length of the cloth
The example of a function is:
The price of a piece of cloth and the length of the cloth.
Step-by-step explanation:We know that a function is a relation in which each element of a set is mapped to a single element of the other set.
i.e. an element has just one image.
1)
The time it takes to mow a lawn and the age of the person mowing the lawn.
This is not a example of function since, the time taken by two person's of different age may be same to mow a lawn.
This means that there is more than one image of a single element i.e. time.
2)
The distance to school and the time you spend at school.
The time one spend at school at different days may be different even if the distance to school is same.
3)
The price of a movie ticket and the height of the customer.
Two person's with different height will buy a movie ticket at the same cost.
Hence, this relation won't be a function.
4)
The price of a piece of cloth and the length of the cloth.
As we know that the price of a cloth is fixed according to the length.
Hence, the relation is a function.
( As corresponding to each price we have a unique length if a piece of clothing )
can someone help answer and explain to me how to solve this? log (lowercase 6) 1/36
The graph of which of the following equations contains the points (2, 3) and (3, 2)? y = x - 1
y = 5 - x
y= 7 - 2x
Which property justifies this statement?
If 4x=20, then x=5.
If rectangle DEFG is dilated by a scale factor of 1/2 with a dilation center of (0, 0), what will be the coordinates of point F'?
You have already saved $55 you earn $9 per hour babysitting you ate saving for a camera that costs $199
Randy solved the following problem: 7/8 + 9/15. He said, "I can add 7 and 9 to get 16 and add 8 and 15 to get 23. The answer is 16/23. " Is Randy correct? Explain your answer.
Alexandra bought a $90000 life insurance policy at $10.98 for a 20 year term. She will pay ___ over 20 years for the premium
The expression on the left side of an equation is shown below.
-5(x+2) +3x =___
If the equation has an infinite number of solutions, which expression can be written in the box on the other side of the equation?
A. -5(x-3) +2x
B. -5x-10
C. x-2x +2 +3x
D. -2(x +5)
After solving the equation, the equivalent equation obtained which has an infinite solution will be equal to -2(x + 5). Hence, option D is correct.
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the given equation in the question,
-5(x + 2) + 3x
Now, solve the equation,
-5x - 10 + 3x
= -5x + 3x - 10
= - 2x - 10
So, the equivalent equation will be,
-2(x + 5), it has an infinite solution because it is the same equation.
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What does y and z equal. I already got x
Among all rectangles that have a perimeter of 156, find the dimensions of the one whose area is largest. write your answers as fractions reduced to lowest terms.
The dimensions of the one whose area is largest is 39 by 39
The formula for calculating the perimeter of a rectangle is expressed as:
P = 2(L + W)
L is the length of the rectangle
W is the width
Given that the perimeter is 156, hence;
2(L + W) = 156
2L + 2W = 156
L + W = 78
W = 78 - L
The area of the rectangle is expressed as:
A = LW
A = L(78-L)
A = 78L - L^2
To get the dimensions of the one whose area is largest, dA/dL = 0
dA/dL = 78 - 2L
0 = 78 - 2L
2L = 78
L = 78/2
L = 39
Recall that 2(L+W) = 156
2(39 + W) = 156
39 + W = 78
W = 78 - 39
W = 39
Hence the dimensions of the one whose area is largest is 39 by 39
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Ben's date of birth is a prime number between 15 and 25. This number has 57 as a multiple.
What date is Ben's birthday?
Davis knows that the area of his square shaped bag is 81 ft sq. What is the length of any side of the bag
How can sums and differences of cubes be identified for factoring?
How to factor this:
6x² + 7x - 5
Please give an explanation on how you did it
Sergio is S years old. Which expression shows how old will he be 7 years from now?
A. 7s
B. 7-s
C. s+7
D. 7s+7
FREE POINTS HELPPP HELPPP WILL GIVE BRAINLEST AND THANKS EASY PLEASE HELP ME
The exponential function in the graph shows the population of Greeville in the years since 2010. What real-world information is given by the point (6, 2707)?
options:
The population in 2006
The population in 2010
The population in 2016
The year in which the population is twice the population in 2010
When is a protractor preferred to a ruler when finding a measurement
A protractor is preferred over a ruler when measuring angles, especially in geometric shapes or when dealing with rotational aspects. While a ruler is great for measuring lengths and distances, it can't accurately measure angles.
For example, let's say you want to measure the angle between two lines on a piece of paper. A ruler can only give you an approximation by comparing lengths, but a protractor will give you an exact measurement of the angle in degrees.
To use a protractor, align the center hole of the protractor with the vertex of the angle. Then, align one side of the angle with the zero-degree mark on the protractor. Finally, read the number where the second side of the angle intersects the protractor scale. This gives you the precise measurement of the angle.
In conclusion, when dealing with angles, a protractor is the preferred tool for accurate measurements, providing exact angles in degrees.
(See attachment please)
What postulate can be used to prove that △ADC≅△CBA ?
Claire's cousin is now 3 times as old as Claire. in 10 years, her cousin will be twice as old as claire. how old is Claire now?
Claire is currently 10 years old.
Explanation:Let's assume that Claire's age is x.
According to the given information, Claire's cousin is now 3 times as old as Claire. This can be represented as Cousin's age = 3x.
In 10 years, Cousin's age will be twice as old as Claire's age. So, we can write the equation:
(3x + 10) = 2(x + 10)
Simplifying the equation:
3x + 10 = 2x + 20
Subtracting 2x from both sides:
x + 10 = 20
Subtracting 10 from both sides:
x = 10
Therefore, Claire is currently 10 years old.
Tyson and his friends go ice skating. Tyson must pay an initial fee of $18.30 plus $4.80 per hour. Write an equation for the cost c Tyson must pay after skating h hours. Solve the equation to find the cost to go ice skating for four hours. Write your answer as an ordered pair.
A, c = 4.80h – 18.30 (4, 0.9)
B. c = 4.80 + 18.30h (4, 78.00)
C. c = 18.30 + 4.80h (4, 37.50)
D. c = 18.30 + 4.80 + h (4, 27.10)
A club with 19 members is to choose three officers president vice president and security secretary treasurer. If each office is to be held by one person and no person can hold more than one office in how many ways can those offices be filled
The baggage limit for an airplane is set at 100 pounds per passenger. thus, for an airplane with 200 passenger seats there would be a limit of 20,000 pounds. the weight of the baggage of an individual passenger is a random variable with a mean of 95 pounds and a standard deviation of 35 pounds. if all 200 seats are sold for a particular flight, what is the probability that the total weight of the passengers' baggage will exceed the 20,000-pound limit?
At a mean of 95 pounds per passenger and standard deviation of 35 pounds, multiplying this with the total number of passengers = 200, results in:
absolute mean = 95 * 200 = 19,000
absolute std dev = 35 * 200 = 7,000
Calculating for the z score:
z = (x – u) / s
where x is sample value = more than 20,000; u is the sample mean = 19,000; s is std dev = 7,000
z = (20,000 – 19,000) / 7,000
z = 0.143
From the distribution tables,
P (z = 0.14) = 0.5557
Therefore a 55.57% chance that it will be more than 20,000 pound limit
Final answer:
Using the Central Limit Theorem, we calculate the probability that the total weight of passengers' baggage exceeds 20,000 pounds for an airplane with 200 passengers to be approximately 0.0217.
Explanation:
To solve this problem, we use the Central Limit Theorem which states that if we have a large enough sample size, the distribution of the sample means will be approximately normally distributed regardless of the original distribution's shape. Given that the mean weight of an individual passenger's baggage is 95 pounds with a standard deviation of 35 pounds, and that there are 200 passengers, we can calculate the mean and standard deviation of the total baggage weight.
The mean total weight, μtotal, is calculated as the product of the mean individual weight and the number of passengers, so μtotal = 95 pounds × 200 = 19,000 pounds. The standard deviation of the total weight, σtotal, is calculated as the standard deviation of the individual weight multiplied by the square root of the number of passengers, so σtotal = 35 pounds × √200 ≈ 494.97 pounds.
Using the standard normal distribution, we find the z-score for the probability that the total weight exceeds 20,000 pounds by subtracting the mean from the limit and dividing by the standard deviation: z = (20,000 - 19,000) / 494.97 ≈ 2.02.
Looking up this z-score in a standard normal table or using a calculator, we find that the probability of the total baggage weight exceeding 20,000 pounds is approximately 0.0217.
if y equals -12 when x equals 9 find y when x equals negative 4
The measure of an angle is forty-four times the measure of a supplementary angle. what is the measure of each angle?
A rectangle has an area of 16 ft2. every dimension is multiplied by a scale factor, and the new rectangle has an area of 64 ft2. what was the scale factor?
Juan used the expression 16 – 9 – 12 + 22 to find his profit for days 2 and 3. He rewrote the expression as 16 + (–9) + (–12) + 22. Juan can use the associative and commutative properties to rewrite the expression again. Explain why he had to use the additive inverse before he could use these properties.
Answer:
Associative property and commutative property true for addition, not true for subtraction.
Step-by-step explanation:
Associative property and commutative property true for addition.
i) a + (b + c) = (a + b) + c ---> Associative property of addition
ii) a + b = b + a --> commutative property of addition.
These properties not true for subtraction.
That's the reason Juan used additive inverse before applying these property.
Hope this will helpful.
Thank you.
[tex]\bold{ a + (b + c) = (a + b) + c } \to[/tex] Associative property of addition
[tex]\bold{a + b = b + a } \to[/tex] commutative property of addition.
As we show above both the property used for the addition and no used for the subtraction, that is why before applying the property Juan applied reverse additives.Learn more:
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Konnor wants to burn 250 calories while exercising for 45 minutes at the gym. on the treadmill, he can burn 6 cal/min. on the stationary bike, he can burn 5 cal/min. if t represents the number of minutes on the treadmill and b represents the number of minutes on the stationary bike, which expression represents the number of calories that konnor can burn on the stationary bike?
Given that b is the number of calories that can be burned using the stationary bike, and the burning rate is 5 cal / min, therefore:
b = 5 t
where t is the time spent on the stationary bike
Answer:
B=5t
Step-by-step explanation:
Maria works for an automobile dealership. She earns a 10% commission on each motorcycle she sells and a 15% commission on each car she sells.
Maria sells a motorcycle for $5,000 and a car for $25,000. What is the total commission that she will earn on the sale of these two vehicles?
The total commission that she will earn on the sale of these two vehicles is $4,250.