So the dimensions of the box are:
Length: 20m
Width: 10m
Height: 10m
We can use the information provided in the problem to set up a system of equations. Let H be the height, L be the length, and W be the width.
From the problem, we know:
L = 2H (the length is twice the height)
W = L - 10 (the width is 10 meters less than the length)
2HW + 2LW + 2LH = 10WH (the surface area is 10 times the width times the height)
We can substitute the first and second equations into the third one to obtain:
2H(2H-10) + 2(2H)(2H-10) + 2(2H)(2H) = 10H(2H-10)
Solving this equation we get H = 10m
With this value we can solve for the other dimensions:
L = 2H = 2 * 10 = 20m
W = L - 10 = 20 - 10 = 10m
So the dimensions of the box are:
Length: 20m
Width: 10m
Height: 10m
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So the dimensions of the box are:
Length: 20m
Width: 10m
Height: 10m
We can use the information provided in the problem to set up a system of equations. Let H be the height, L be the length, and W be the width.
From the problem, we know:
L = 2H (the length is twice the height)
W = L - 10 (the width is 10 meters less than the length)
2HW + 2LW + 2LH = 10WH (the surface area is 10 times the width times the height)
We can substitute the first and second equations into the third one to obtain:
2H(2H-10) + 2(2H)(2H-10) + 2(2H)(2H) = 10H(2H-10)
Solving this equation we get H = 10m
With this value we can solve for the other dimensions:
L = 2H = 2 * 10 = 20m
W = L - 10 = 20 - 10 = 10m
So the dimensions of the box are:
Length: 20m
Width: 10m
Height: 10m
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2x - 3 y = -1 y = x - 1 Solve each system of equations. Show all your work.
x = 4, y = 3 for the given equation 2x - 3 y = -1 , y = x - 1 .
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. The meanings of the word equation and its cognates in various languages can vary slightly. For instance, in French, an equation is defined as having one or more variables, whereas in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign.Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfil the equality are known as the equation's solutions.Given data :
2x - 3 y = -1
y = x - 1
In a system of equations, there are multiple equations present. We actually look for the point at which these equations are identical when we attempt to solve a system of equations problem. In order to solve such an issue, we typically employ the substitution method, which involves inserting the values of one variable into the initial expression in order to determine the value of the second variable.
3y=2x+1
y= (2/3)x + 1/3 = x-1
x/3 =4/3
x = 4, y=3
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Draw number line to show the following
0>x≥5
The graph of the inequality 0 > x ≥ 5 can be seen on the image at the end.
How to graph the inequality?Here we want to graph the following inequality:
0 > x ≥ 5
So, x is strictly larger than 0 and smaller than or equal to 5.
Because x = 0 is not a solution, we will draw an open circle at x = 0.
Then a line that goes to the right until x = 5, where we will draw a closed circle, because that value belongs to the solution set, then the inequality is the one you can see below.
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I need help asap. I attached a imagine of the question.
Answer:
[tex]\boxed{n = - 5}[/tex]
Step-by-step explanation:
[tex]\textrm{We have the following equation:}\\\\\dfrac{n}{5}+\dfrac{\left(n-3\right)}{2}=n\\\\\textrm{ and we are asked to solve for n}[/tex]
Solution Steps
Multiply throughout by 10 which is the LCM of the denominators, 5 and 2
[tex]\dfrac{n}{5}\cdot \:10+\dfrac{n-3}{2}\cdot \:10=n\cdot \:10\\\\2n + 5(n-3) = 10n\\[/tex]
Expand the brackets: [tex]5(n-3) = 5n - 15\\\\[/tex]
The equation becomes:
2n + 5n - 15 = 10n
Add similar terms:
7n - 15 = 10n
Move 15 to the right side:
7n = 10n + 15
Move 10 to the left side
7n - 10n = 15
- 3n = 15
n = -15/3
[tex]\boxed{n = - 5}[/tex]
if k+7=16 then find the value of 8k-72
Answer:
0
Step-by-step explanation:
[tex]k + 7 = 16\\k = 9\\8k - 72\\8(9) - 72 = 0[/tex]
how to graph
y=-1/2x + 3
y=5
Answer:
The graph would look like this
Step-by-step explanation:
The length of a rectangle is 6 less than twice its width. The perimeter is 90. Find the dimensions of the rectangle
The length of the rectangle is 20 and the width is 13.
What are the dimensions?The perimeter of a rectangle = 2(length + width)
Width = w
Length = 2w - 6
90 = 2(w + 2w - 6)
In order to determine the value of w, take the following steps:
Divide both sides of the equation by 2
90/2 = w + 2w - 6
45 = w + 2w - 6
Combine and add similar terms:
45- 6 = w + 2w
39 = 3w
Divide both sides of the equation by 3
w = 39/3
w = 13
In order to determine the length, substitute for w in the equation that represents the length.
Length = 2(13) - 6
= 26 - 6
= 20
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I took a random sample of size 49 students score from their sampling distribution test. The
score was selected from the Regular Statistics class. The mean of the score of the population of
Regular statistics is 63 and standard deviation is 14. What is the probability in the sample selected will have mean score more than 65.
The probability of a sample mean more than 65 is given as follows:
0.1587 = 15.87%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 63, \sigma = 14, n = 49, s = \frac{14}{\sqrt{49}} = 2[/tex]
The probability of a sample mean above 65 is one subtracted by the p-value of Z when X = 65, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (65 - 63)/2
Z = 1
Z = 1 has a p-value of 0.8413
1 - 0.8413 = 0.1587 = 15.87%.
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La base de un cuadrado sin marco mide el doble de su altura si el marco tiene 2 pulgadas de ancho y su área es de 208 pulgada cuadradas encuentre las dimensiones del cuadrado sin marco
If the frame has 2 inches of width and its area is 208 inches of square. The dimensions of square without frame is 6.75 and 13.50.
Let the width of rectangle without frame is b.
Let the height of rectangle without frame is h.
Since the base of a square without frame is the double of its height. So
b = 2h...............(1)
The frame has 2 inches of width, so;
The width of rectangle with frame = b + 4
The height of rectangle with frame = h + 4
The area of the rectangle with frame = 208 inches of square
The formula of area of rectangle
A = Height × Width
(h + 4) × (b + 4) = 208
Putting the value of b from the equation 1
(h + 4) × (2h + 4) = 208
Simplify
h(2h + 4) + 4(2h + 4) = 208
2h^2 + 4h + 8h + 16 = 208
2h^2 + 12h + 16 = 208
Subtract 208 on both side, we get
2h^2 + 12h - 192 = 0
Taking common 2 from the equation, we get
h^2 + 6h - 86 = 0
After factoring the equation we get
h = (−3+√95, −3−√95)
h = 6.75, -12.75
The height can't be negative so we use the positive value of h.
Now putting the value of h in the equation 1.
b = 2×6.75
b = 13.50
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The complete question is:
The base of a square without frame is the double of its height, if the frame has 2 inches of width and its area is 208 inches of square. Find the dimensions of the square without frame.
What is the domain of the function
f(x) =
X+2
x≤-B
*>B
x2-6
Answer:
x ≥ -6
Step-by-step explanation:
Answer: x ≥-6
explanation: im pretty good at math
Use the long division method to find the result when 8x^{3}+6x^{2}+26x-128x
3
+6x
2
+26x−12 is divided by 4x-14x−1.
Answer:
4x^2-3x+1+18?=2x+3
Step-by-step explanation:
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An object is dropped from 28 feet below the tip of the pinnacle atop a 928-ft tall building. The height h the object after t seconds is given by the equation h=-16t^(2)+900. Find how many seconds pass before the object reaches the ground.
Answer: it takes 7.5 seconds for the object to reach the ground.
Step-by-step explanation:
The equation for the height of the object is h=-16t^2+900. To find the time when the object reaches the ground, we need to find the value of t when h=0.
Therefore, we can set h=-16t^2+900 = 0 and solve for t:
-16t^2+900 = 0
-16t^2 = -900
t^2 = 56.25
t = sqrt(56.25)
t = 7.5
So, it takes 7.5 seconds for the object to reach the ground.
a researcher reported that for 100 college students, the mean was 80 and the standard deviation was 12.6. how is the standard deviation best interpreted?
It can be interpreted as the average distance between each data point and the mean value of 80 for the 100 college students.
Standard deviation is a measure of the spread of values in a set of data, calculated as the square root of its variance. It indicates how much variation or dispersion there is from the mean of the set.
The standard deviation is a measure of the variability or dispersion of the data set around the mean. In this case, it can be interpreted as the average distance between each data point and the mean value of 80 for the 100 college students.
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Find the percent of change when 51 is increased to 98. If necessary, round your answer to the nearest tenth.
a
48% decrease
b
48% increase
оооо
Ос
92. 296 decrease
Od
92. 29 increase
The percent of change when 51 is increased to 98, then there have increment of 92%. So the option d is correct.
The difference between a new and old amount, given as a percentage, is known as a percent change.
Calculating percent change involves determining the difference between the old and new quantities, dividing that difference by the old quantity, and multiplying that result by 100.
The number 51 is raised to 98; calculate the percentage change.
To start, subtract the new quantity from the previous one to determine the difference. 98 - 51 = 47, therefore the difference is 47.
The difference, 47, is then divided by the old amount, 51, yielding a result of 47/51=0.92.
Lastly, multiply the decimal by 100 × 0.92 to get the percentage change, which is increment of 92%.
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To weave a bracelet, Charlene needs 7 pieces of brown thread. Each piece of thread must be 1/3 yard long. How many thread should she buy to weave the bracket?
Charlie must buy 7/3 yards long brown thread to weave a bracelet.
Based on number of pieces of brown thread and length of each piece, the formula that will be formed is -
Length of thread required = number of threads × length of each piece
Keep the values in formula to the length of piece required to weave a bracelet
Length of thread required = 7 × 1/3
Performing multiplication on Right Hand Side of the equation
Length of thread required = 7/3 yards
Thus, 7/3 yards of length is required to weave the bracelet.
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*PLEASE HELP SOON* Evaluate 5^x for each given value of x.
Each of the function should be evaluated as follows;
When x = 2, 5^x = 25.When x = 1, 5^1 = 5.When x = 0, 5^0 = 1.When x = -1, 5^-1 = 1/5.How to evaluate the function for each given value of x?In Mathematics, the valid and true solutions to any function are referred to as the domain (input value) and they can be determined by substituting the x-values contained in the table into the function.
When x = 2, the range (output value) for this function is given by:
Function, f(2) = 5^x = 5^2 = 25.
When x = 1, the range (output value) for this function is given by:
Function, f(1) = 5^x = 5^1 = 5.
When x = 0, the range (output value) for this function is given by:
Function, f(0) = 5^x = 5^0 = 1.
When x = -1, the range (output value) for this function is given by:
Function, f(x) = 5^x = 5^-1 = 1/5.
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2x²+4x+5=ax²+(2b-6)x+c what does a,b,c represent
Answer: A=2 B=4 C=5
Step-by-step explanation:
Write a quadratic given a vertex (11,2) and a point (9,3)
The equation of a quadratic equation with a vertex and a point is
y = 1/4 (x - 11)² + 2
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 6 is an equation.
We have,
Vertex = (11, 2)
Point = (9, 3)
The equation of a quadratic equation with a vertex and a point is
y = a (x - h)² + k
Where (h, k) is the vertex and (x, y) is the point.
Now,
(11, 2) = (h, k)
(9, 3) = (x, y)
Substitute.
y = a (x - h)² + k
3 = a (9 - 11)² + 2
3 = a x 4 + 2
3 = 4a + 2
3 - 2 = 4a
a = 1/4
Now,
The equation of a quadratic equation is y = 1/4 (x - 11)² + 2.
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Scholars measured how two different class plants grew over a week. They wrote the equations below to represent the height of each plant.
● Bean plant: h = 0.25d, where h is the height in inches and d is the number of days
● Sunflower: h = 10 + 0.02d, where h is the height in inches and d is the number of days
Brie says that both plants have a proportional relationship between the height and number of days because each plant grows by the same amount each day.
Do you agree or disagree with Brie? Explain why
I disagree with Brie.
Only the bean plant has a proportional relationship. The sunflower does not have a proportional relationship.
How to determine whether to agree or disagree with Brie?In a proportional relationship, the ratio of the dependent variable (height) to the independent variable (number of days) is constant. In this case, the ratio of height to number of days is not constant for both plants.
For the bean plant, the ratio of height to number of days is 0.25, which is constant. This means that the bean plant grows by 0.25 inches per day.
For the sunflower, the ratio of height to number of days changes as the number of days increases, it starts with 10 and increases by 0.02 each day. This means that the growth rate of the sunflower is not constant, it starts with 10 and increases by 0.02 inches per day.
Thus, I disagree with Brie.
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3 (2 x - 7) = 3
How many solutions does this equation have?
Answer:
It has one solution, x = 4
Step-by-step explanation:
[tex]3(2x-7) = 3\\2x-7 = \frac{3}{3} \\2x-7 = 1\\2x = 8\\x = 4[/tex]
No other answer would work
Find the inequality represented by the graph!
The inequality is y ≥ 1/2x.
How to find the calculation?We must first identify the linear equation that describes the line in the graph in order to determine the inequality it reflects.
So, using the two points (0, 0) and (2, 1), we first get the slope of the line:
m = y2 - y1 /x2 - x1 = 1-0 / 2-0 = 1/2
Now, we can determine the linear expression using one point, the slope, and the slope-point formula.
y - y1 = m( x - x1)
y - 0 = 1/2(x - 0 )
y = 1/2 x
Then, to evaluate the linear equation, we only need to select a test point from the shaded region, which will be (0,1):
y = 1/2 x
1 = 1 / 2 (0)
1 = 0
Because 1 is greater than 0 and the line is solid, we can infer that the inequality sign is in the proper position.
Therefore, the inequality is y ≥ 1/2x.
The Complete Question is inequality.
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The graph of y = In(x) was transformed by shifting 8 units left and 12 units up. Write an equation
The equation of the translated function for this problem is given as follows:
y = ln(x + 8) + 12.
What are the translation rules?The four translation rules are defined as follows:
Left a units: g(x) = f(x + a).Right a units: g(x) = f(x - a).Up a units: g(x) = f(x) + a.Down a units: g(x) = f(x) - a.The parent function in this problem is given as follows:
y = ln(x).
The translations in this problem, and their effects, are given as follows:
8 units left: x -> x + 8.12 units up: y -> y + 12.Hence the translated function is defined as follows:
y = ln(x + 8) + 12.
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Determine if the given point is a solution of the system of inequalities.
Help please.
The inequality equations is
a) The point ( -9 , 4 ) lies on the inequality relation
b) The point ( 6 , -2 ) lies on the inequality relation
c) The point ( 0 , -4 ) does not lie on the relation
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
a)
Now , let the first point be represented as P ( -9 , 4 )
The shaded region is below 4 in the y axis and less than -4 in the x axis
So , the point ( -9 , 4 ) does lies on the inequality equation graph
b)
Now , let the first point be represented as Q ( 6 , -2 )
The shaded region is below -8 in the y axis and less than 8 and more than 4 in the x axis
So , the point ( 6 , -2 ) does lies on the inequality equation graph
c)
Now , let the first point be represented as R ( 0 , -4 )
The shaded region is above -8 in the y axis and more than -4 in the x axis and less than -1
So , the point ( 0 , -4 ) does not lie on the inequality equation graph
Hence , the inequality equations is solved
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If $\angle A=20^\circ$ and $\angle AFG=\angle AGF,$ then how many degrees is $\angle B+\angle D?$
The angles b and d have 80° degrees.
Trigonometry is the branch of mathematics that studies and defines the relations between the side lengths and angles of a triangle.
One key fact to know in all trigonometry problems is that all angles within a normal triangle = 180 degrees.
By creating algebraic equations based on the information given in the question, we can find missing values using this key fact.
Given:
Angle a = 20 deg
Angle b = Angle d = x
x = ?
We know that since two angles are equal, it is an isosceles triangle.
Using algebra and the given information, we create an equation:
20+2x=180
2x=180-20
2x=160
x=80
Therefore, we know that angles b and d are 80° degrees.
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A y=x
The graph shown above is the graph of which parent function after a vertical shift up 1 unit?
y=x²
y=x³
Dy=x²
B
1
C
X
The equation for the graph after the shift would be y = x + 1. The answer is y = x + 1.
What happens when a function is shifted vertically?
Because this transformation involves adding a positive or negative constant to the function, a vertical shift, which moves the graph up or down, is the simplest shift. In other words, regardless of the input, the output result of the function receives the same constant.
The y-value adjusts when a function shifts vertically. While the y-value modifies the shift's magnitude, the x-value remains constant.
We add the value to the y-term if it changes upward. We shall deduct that amount from the y-term if it shifts downward.
The simplest transformation is a vertical shift, which entails moving the graph up or down. This is because this transformation only requires changing the function's sign from positive to negative.
The only variable that alters in vertical shifts of the fundamental linear equation y = mx + b is the b value, or the y-intercept.
The graph shown above is the graph of the parent function y=x after a vertical shift up 1 unit.
Hence, The equation for the graph after the shift would be y = x + 1. The answer is y = x + 1.
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I NEED HELP ON THIS ASAP!!!!
Answer:
see below
Step-by-step explanation:
v=πr² (h/3)
h=3v/πr²
original equation measures v using bottom circle area multiply the height.
the equation for the height reverses the multiplication using volume divided by the area, so the result is a linear measurement.
In the diagram below, Ray AB bisects Angle CAD. Solve for x and the measure of Angle CAD. Show all of your work.
The inequality d < 4. 75 represents the prices d in dollars that Paige is willing to pay for popcorn. The inequality d < 8. 00 represents the prices d in dollars that Paige is willing to pay for a movie ticket. At how many theaters would Paige be willing to buy a ticket and popcorn?
At two theaters Paige would be willing to buy a ticket and popcorn.
Consider the following table that shows ticket and popcorn prices at five movie theater chains.
Here, the inequality d < 4. 75 represents the prices d in dollars that Paige is willing to pay for popcorn.
And the inequality d < 8. 00 represents the prices d in dollars that Paige is willing to pay for a movie ticket.
To find: the number of theaters that would Paige be willing to buy a ticket and popcorn
We can observe that the number of theaters that has the movie ticket price less than 8 dollars are two.
The number of theaters that has the popcorn price less than 4.75 dollars are three.
And the number of theaters that has the popcorn price less than 4.75 dollars as well as the movie ticket price less than 8 dollars are two.
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Determine whether each pair of equations are equivalent. Explain your answer. 5x − 4 + 3x = 8 and 8x = 12
what is (5x+6)-(2x+5).
John was able to assemble 10 bicycles in 8 hours. Considering that he is consistent assembling each bicycle, how many bicycles can John assemble in 1 hour?
To find out how many bicycles John can assemble in 1 hour, you can use the formula:
rate = work/time
where rate is the number of bicycles John can assemble in 1 hour, work is the total number of bicycles he assembled, and time is the total time it took him to assemble the bicycles.
In this case, the work is 10 bicycles and the time is 8 hours. So, we can substitute these values into the formula:
rate = 10 bicycles / 8 hours
rate = 1.25 bicycles/hour
So John can assemble 1.25 bicycles in 1 hour, assuming he works at a consistent pace.