The equations that have the same value of x as the original equation are: 18 x minus 9 = 72, 3 (6 x minus 3) = 72 and x = 4.5
Identifying the equations with the same solutionFrom the question, we have the following parameters that can be used in our computation:
Three-fifths (30 x minus 15) = 72
Express properly
So, we have
3/5(30x - 15) = 72
This gives
18x - 9 = 72
Factor out 3
So, we have
3(6x - 3 = 72)
When solved, we have
x = 4.5
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A piece of timber is x cm long. how long would 10 pieces of timber be put together in a line?
Answer:
10x cm
Step-by-step explanation:
e.g.
5cm cm x 10 = 50cm
--> 10x cm
The length of the 10 pieces together will be, 10x.
What is length?The length is the distance between the extreme ends of the object.
It is known that the length of one piece of timber is x cm.
Multiply 10 and x to determine the total length of 10 pieces of timber together.
10·x=10x
Thus, the total length of 10 pieces of timber will be 10x cm.
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Select the dot plot with the greatest variability.
OA.
OB.
O C.
O D.
-
32 34 36 38 40 42
30 32 34 36 38 40
5
← PREVIOUS
11 13 15
Help me
Dot plot A has a range of 4 and the data is very clustered together.
The correct answer to the given question is option 3.
The dot plot with the greatest variability can be determined by analyzing the spread of data on the plot. Variability is the extent to which data varies. A higher range of data will have a larger variability, whereas a smaller range will have less variability.
A dot plot is an effective way to visualize data on a number line where each data point is represented by a dot. It helps to identify the spread and distribution of data.
Among the four dot plots given, the plot with the greatest variability is the plot (C) with data range -32, 34, 36, 38, 40, and 42.
The range of data on dot plot C is 74, which is the largest range among all the given plots. On dot plot C, the highest and the lowest data points are -32 and 42, respectively.
Therefore, this dot plot has the greatest variability of all the given plots.Dot plot O and Dot plot D have similar data ranges, but they have different variabilities.
Dot plot O has a lower variability compared to plot D. Dot plot B has a range of 5, but the rest of the plots have ranges greater than 5.
Dot plot A has a range of 4 and the data is very clustered together.
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Which values of x, if any, prove that the graph below is not a function?
Answer:
3
Step-by-step explanation:
For a graph not to be a function, it means that a particular value of x has more than one corresponding value of y. Looking at the graph, at the point where x = 3 on the horizontal axis, there are so many value of y. Plus, the graph below is not a function at x = 3
The correct option is 3
Definition: To solve a problem, we often______
the given information into algebraic expressions and
Example: The phrase "4 more than twice a number' becomes 2n + 4'.
To solve a problem, we often Translate the given information into algebraic expressions and equations.
Step-by-step explanation:
Consider the provided statement.
In order to solve a mathematical problem, we often translate the given information into algebraic expressions and equations.
For example: “6 less than twice a number"
We first need to translate it.
This can be translated as: 2n-6
Where n represents the number.
Hence, the complete statement is To solve a problem, we often Translate the given information into algebraic expressions and equations.
is it possible to choose (2n 1)^2 points in the disc of radius n such that the distance between any two of them is greater than 1?
Answer: its (4f 5) ^3
Step-by-step explanation:
3) let’s say katie’s bike cost $100. a) if timothy’s bike is 20% the cost of katie’s, what does his bike cost?
a) Timothy's bike costs $20.It's important to note that the given percentage value represents a proportion or fraction of the original cost, allowing us to calculate the specific cost
To find the cost of Timothy's bike, we need to calculate 20% of Katie's bike cost.
20% of $100 can be calculated by multiplying $100 by 0.20:
20% * $100 = $20.
Therefore, Timothy's bike costs $20.
To calculate 20% of $100, we multiply $100 by the decimal equivalent of 20%, which is 0.20:
20% * $100 = 0.20 * $100 = $20.
In this scenario, Timothy's bike is priced at 20% of Katie's bike cost. This means that Timothy's bike is relatively less expensive compared to Katie's bike. It's important to note that the given percentage value represents a proportion or fraction of the original cost, allowing us to calculate the specific cost of Timothy's bike based on the given percentage relationship.
Based on the given information, Timothy's bike costs $20, which is 20% of Katie's bike cost.
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The sum of two consecutive integers is 129. Find both integers.
Given that,
the two numbers are consecutive
The two numbers are
x and x + 1
Sum of the numbers = 129
x + (x + 1) = 129
x + x + 1 = 129
2x = 129 - 1
2x = 128
x = 128/2
x = 64
Therefore, the two numbers are x = 64 and x + 1 = 65
What does irrational mean
given the function f(x)=-5|x+1|+3 for what values of c is f (x) =-12
Answer: x=2 and x=-4
Step-by-step explanation:
What shape is the base of a triangular prism?
Answer: A triangular prism has a base of a rectangle as shown in this picture.
Step-by-step explanation: If your having trouble recognizing prisms here's a tip. All prisms have a rectangular base. :)
Suppose a company wants to introduce a new machine that will produce a marginal annual savings in dollars given by S '(x)= 175 - x^2, where x is the number of years of operation of the machine, while producing marginal annual costs in dollars of C'(x) = x^2 +11x. a. To maximize its net savings, for how many years should the company use this new machine? b. What are the net savings during the first year of use of the machine? c. What are the net savings over the period determined in part a?
a) To maximize its net savings, the company should use the new machine for 7 years. b) The net savings during the first year of use of the machine are $405 (rounded off to the nearest dollar). c) The net savings over the period determined in part a are $1,833.33 (rounded off to the nearest cent).
Step-by-step explanation: a) To determine for how many years should the company use the new machine to maximize its net savings, we need to find the value of x that maximizes the difference between the savings and the costs.To do this, we need to first calculate the net savings, N(x), which is given by:S'(x) - C'(x) = 175 - x² - (x² + 11x) = -2x² - 11x + 175To find the maximum value of N(x), we need to find the critical values, which are the values of x that make N'(x) = 0:N'(x) = -4x - 11 = 0 ⇒ x = -11/4The critical value x = -11/4 is not a valid solution because x represents the number of years of operation of the machine, which cannot be negative. (i.e., not use it at all).However, this answer does not make sense because the company would not introduce a new machine that it does not intend to use. Therefore, we need to examine the concavity of N(x) to see if there is a local maximum in the feasible interval.
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A computer costs $600. You pay $150 and will pay the rest in 6 equal installments. How much will each payment be?
During 'one game, Mary's coach measures the time she takes while running around the bases. Mary takes a total of 20 s to run the total distance of 240ft. If a function compares the distance she travels to the time she spends running, what is the range of this function?
The range would include all distances that Mary can possibly travel in 20 seconds,
The range of a function represents the set of all possible output values that the function can produce. In this case, the function compares the distance Mary travels to the time she spends running.
Mary takes a total of 20 seconds to run the distance of 240 feet. Therefore, the function's range is the set of all possible distances Mary can travel within that time frame.
Since Mary's time is fixed at 20 seconds, the range of the function would be determined by the distances she can cover in that time.
Mary's speed can vary, so the distance she can cover depends on her running pace. However, since we don't have specific information about her speed or running patterns, we can't determine the exact range of the function in terms of specific distances.
In general, the range would include all distances that Mary can possibly travel in 20 seconds, which could range from 0 (if she stands still) to a maximum distance that depends on her speed.
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An acute angle, θ, is in a right triangle such that sin of theta is equal to 3 over 8 period What is the value of cot θ?
square root of 55 over 3
the quantity 3 times the square root of 55 end quantity over 55
square root of 55 over 8
the quantity 8 times the square root of 55 end quantity over 5
We want to find the value of cot(θ) given that sin(θ) = 3/8 and θ is an angle in a right triangle, we will get:
cot(θ) = (√55)/3
So we know that θ is an acute angle in a right triangle, and we get:
sin(θ) = 3/8
Remember that:
sin(θ) = (opposite cathetus)/(hypotenuse)hypotenuse = √( (opposite cathetus)^2 + (adjacent cathetus)^2)Then we have:
opposite cathetus = 3
hypotenuse = 8 = √(3^2 + (adjacent cathetus)^2)
Now we can solve this for the adjacent cathetus, so we get:
adjacent cathetus = √(8^2 - 3^2) = √55
And we know that:
cot(θ) = (adjacent cathetus)/(opposite cathetus)
Then we get:
cot(θ) = (√55)/3
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A firm is expected to pay a dividend of $2.55 next year and $2.70 the following year. Financial analysts believe the stock will be at their price target of $40 in two years. Compute the value of this stock with a required return of 12.5 percent. (Round your answer to 2 decimal places.)
The required return rate is 12.5%. The value of the stock is calculated by discounting the future dividends and the price target back to the present value that is $36.0153
To compute the value of the stock, we can use the formula for the dividend discount model:
Value of Stock = Dividend / \((1 + Required Return Rate)^n\) + Dividend / \((1 + Required Return Rate)^{(n+1)}\) + Price Target / \((1 + Required Return Rate)^{(n+2)}\)
In this case, the dividends are $2.55 and $2.70, the required return rate is 12.5%, and the price target is $40. The dividends are discounted back to the present value using the required return rate, and the price target is discounted back two years. By plugging in the values into the formula and calculating, we can find the value of the stock.
Using the given values, the value of the stock with a required return of 12.5% is calculated as follows:
Value of Stock = $2.55 /\((1 + 0.125)^1\) + $2.70 / \((1 + 0.125)^2\) + $40 /\((1 + 0.125)^2\)
Value of Stock ≈ $36.0153
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anyone know how to do this??
Answer: the answer to the first question is B and the answer to the other question is C
Step-by-step explanation: if im right plz mark as brainliest. Hope this helps :)
all of the following expressions are equivalent except x-77+(-x)-x + 77-x
Answer
Option A is the answer.
Explanation
To know which one is not equivalen to the others, we will need to solve and simplify each of them
Option A
x - 7 = x - 7
Option B
7 + (-x) = 7 - x
Option C
-x + 7 = 7 - x
Option D
7 - x = 7 - x
Hope this Helps!!!
You have a coupon for 30% off your total order.
You buy a shirt, shoes, and a hat. The shirt is
$15, the shoes are $65, and the hat is $14. The
tax rate is 6%, taken on the subtotal. How much
do you pay?
Answer:
you pay $69.74
Step-by-step explanation:
total cost without coupon: 15+65+14 = 94
apply the 30% discount ⇒ 94 × .30 = 28.20
subtract the savings ⇒ 94.00 - 28.20
total, after coupon, before tax ⇒ 65.80
apply 6% tax to 65.80 ⇒ 65.8 × .06 ⇒ 3.94
add tax to cost after coupon ⇒ 65.80 + 3.94
you pay $69.74
Bear has $500 in his savings account, and Mrs. Killcrease has $900 in hers. Bear is adding $50 per month, whereas Mrs. Killcrease is contributing $30 per month. Write an equation that represents the amount in eac savings account and determine when they have the same amount.
Bears equation in slope intercept form with no spaces: __
Mrs. Killcreases equation in slope intercept form with no spaces: ___
After $___ months, both will have $___ in their savings account.
Answer: they meet at \(20\) months. Bear: \(50x20=1000\) \(1000+500=1500\) Mrs. Killcrease: \(30x20=600\) \(900+600=1500\)
Step-by-step explanation:
Complete the sequence of transformations that produces △X'Y'Z' from △XYZ.
A clockwise rotation
° about the origin followed by a translation
units to the right and 6 units down produces ΔX'Y'Z' from ΔXYZ.
A clockwise rotation 90° about the origin followed by a translation
2 units to the right and 6 units down produces Δ X'Y'Z' from Δ XYZ
There are four types of transformations: reflection, rotation, translation, and dilation.
What are transformations?Translation, rotation, reflection, and dilation are the four primary categories of transformation.
* Let's update the translation and rotation.
-If point (x, y) rotates 90 degrees counterclockwise with respect to the origin, then Its picture is (-y , x)- If point (x, y) rotated 180 degrees counterclockwise with respect to the origin Its picture is (-x , -y)- If point (x, y) rotates 270 degrees counterclockwise with respect to the origin Its picture is (y , -x)- If point (x, y) rotates 90 degrees clockwise with respect to the origin Its picture is (y , -x)- If point (x, y) rotates 180 degrees clockwise with respect to the origin Its picture is (-x , -y)If the point (x, y) rotated.
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Answer:clockwise rotation 90
translation is 2 units
Step-by-step explanation:
I need help... this is from a textbook Jamal and Moshe began a business with a capital of S7500. If Jamal furnished half as much capital as Moshe, how much did each furnish?
Answer:
Moshe made $1875 and Jamal made $5625
Step-by-step explanation:
divide it in half, then divde Moshe's half in half because he only made half as much,
hope this helps and remember to mark brainliest
Moshe furnishes $5000 and Jamal furnishes $2500 of the capital. Computed by solving the linear equation x + x/2 = 7500, where x is the capital furnished by Moshe.
What are linear equations?Linear equations are an equation involving constants and variables, where variables are raised to a power of not greater than 1.
How do we solve the given question?We are informed that Jamal and Moshe starts a business with a capital of $7500. Also, we are informed that Jamal furnishes half as much capital as Moshe does.
We will try to make a linear equation and solve for it to find the capital furnished by each of them.
Let the capital furnished by Moshe be $x.
Jamal furnishes half as much capital as Moshe does.
∴ Capital furnished by Jamal = 1/2 of Moshe's capital = 1/2 of $x.
∴ Jamal's capital + Moshe's capital = Total capital furnished
We know the total capital is $7500.
∴ Our linear equation is: 1/2 of $x + $x = $7500.
Now we solve this equation in the following ways:
or, (1/2)*x + x = 7500
or, x/2 + x = 7500
or, (x + 2x)/2 = 7500
or, 3x/2 = 7500
or, x = (7500*2)/3 = 15000/3 = 5000.
∴ x = 5000.
∴ Moshe's share = $x = $5000
Jamal's share = 1/2 of $x = 1/2 of $5000 = $2500.
∴ Moshe furnishes $5000 and Jamal furnishes $2500 of the capital. Computed by solving the linear equation x + x/2 = 7500, where x is the capital furnished by Moshe.
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What will be the coordinates of point M of the image after the rotation?
0 (-4, 1)
0 (-1,4)
O (1-4)
O (4,1)
Equations of parallel lines
Answer: c
Step-by-step explanation:
In order to be parallel, the slope must be the same. This means slope is 2
Now one of the point is 5,-1, so do 2x5 + x = -1, so x = -11
meaning b is -11
so the equation should be y=2x-11
Which of the following numbers are perfect squares of even numbers?
121, 225, 784, 841,576,6561
Answer:
784=28....576=24
Step-by-step explanation:
Answer:
121 , 225 , 841 , 6561
Hope this will help you
consider an infinitely long three-sided triangular enclosure with side lengths 2 cm, 3 cm, and 4 cm. the view factor from the 2 cm side to the 4 cm side is
The view factor from the 2 cm side to the 4 cm side of the infinitely long three-sided triangular enclosure is approximately 0.5.
The view factor (F) from Surface A to Surface B can be calculated using the formula:
F = A / (A + B)
where A and B are the areas of Surface A and Surface B, respectively.
The area of a triangle can be calculated using Heron's formula:
Area = sqrt(s * (s - a) * (s - b) * (s - c))
where s is the semi-perimeter of the triangle and a, b, and c are the side lengths of the triangle.
For Surface A:
a = 2 cm
b = 3 cm
c = 4 cm
s = (a + b + c) / 2 = (2 + 3 + 4) / 2 = 4.5 cm
Area_A = sqrt(4.5 * (4.5 - 2) * (4.5 - 3) * (4.5 - 4))
= √(4.5 * 2.5 * 1.5 * 0.5)
=√(5.625) ≈ 2.37 cm²
For Surface B:
a = 2 cm
b = 4 cm
c = 3 cm
s = (a + b + c) / 2 = (2 + 4 + 3) / 2 = 4.5 cm
Area_B = √(4.5 * (4.5 - 2) * (4.5 - 4) * (4.5 - 3))
= √(4.5 * 2.5 * 0.5 * 1.5)
=√(5.625) ≈ 2.37 cm²
Now we can calculate the view factor (F):
F = Area_A / (Area_A + Area_B)
= 2.37 / (2.37 + 2.37)
≈ 0.5
Therefore, the view factor from the 2 cm side to the 4 cm side of the infinitely long three-sided triangular enclosure is approximately 0.5.
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At an online fruit dealer, it costs $39 for 75 cases of bananas. What is the unit price?
Answer:
$0.52 cents per banana. $39 divided by the 75 bananas
Step-by-step explanation:
Answer:
$0.52
Step-by-step explanation:
When finding the unit price, we use divide the certain number of units of an item by the number of units
So for this question we will divide 39/75 to get a result of $0.52
Is the perimeter of an equilateral triangle proportional to the side length of the triangle?Explain your reasoning.
Answer:
Yes
Step-by-step explanation:
I think so because it's the same on both sides.
I don't know man. I'm not the best at math :)
help me plzzzzzz tyyyyyyyyyy
Answer:
your answer is B.
Step-by-step explanation:
mode is 76, mean is 79, the median is 76.
I will give u brainliest if u ans correctly
plzz help
it easy but still
Answer:
It would be A 0.20mm
Step-by-step explanation:
It would be A because there are 12 coins in that stack with the stack's height being 2.40
Divide 2.40 by 12
2.40/12=0.20
Hope this helps
9) A computer generates a random, 3-digit number from 100-999. How many numbers can be generated that are divisible by 2 and 7?
Let consider the numbers between 100 to 199;
The numbers which are divisible by 2 and 7 are 112, 126, 140, 154, 168, 182 and 196.
Total 7 numbers.
Similarly, between 200 to 299, 300 to 399, 400 to 499, 500 to 599, 600 to 699, 800 to 899 and 900 to 999; have 7 such numbers. And between 700 and 799 8 numbers including 700.
So there are (8 x 7) + 8 = 64 numbers