Let's call the width of the rectangle "w".
According to the problem, the length of the rectangle is 12 meters more than 5 times the width, so we can write that as:
L = 5w + 12
And the area is given as 32 square meters, so we can write that as:
A = L * w = 32
Now we have two equations:
5w + 12 = L
L * w = 32
We can use the first equation to substitute the value of L in the second equation:
L = 5w + 12
32 = (5w + 12) * w = 5w^2 + 12w
Expanding the right side of the equation, we get:
32 = 5w^2 + 12w
Now we have a quadratic equation that we can solve for w. To do this, we can use the quadratic formula:
w = (-b ± √(b^2 - 4ac)) / 2a
where a = 5, b = 12, and c = -32. Plugging in these values, we get:
w = (-12 ± √(12^2 - 4 * 5 * -32)) / (2 * 5)
w = (-12 ± √(144 + 640)) / 10
w = (-12 ± √(784)) / 10
w = (-12 ± 28) / 10
w = (16 / 10) or ( -40 / 10)
w = 1.6 or -4
Since the width cannot be negative, the width must be 1.6 meters.
what is the minimum value of y=x^2+36/5
Answer:
(36/5)
Step-by-step explanation:
y=x^2+36/5
Since x is squared, the result will always be a positive number, regardless of the actual value of x. Starting with a value of x of zero, the x^2 term will only grow as one moves away from 0. E.g., (-1)^2 = 1, (-2)^2 = 4, etc.
So the minium for this equation will occur when x = 0. It only gets larger from that point. The minimum is (36/5).
See the attached graph.
15 solids and 15 liquids found in the kitchen.
Please help.
15 liquids that can be found in a kitchen include:
WaterMilkJuice Cooking oil VinegarWineSoy sauceHoneySoupKetchupMustardMayonnaiseSalad dressingEggnogCocktail mixers15 solids in a kitchen are:
FlourSugarSaltRiceBaking sodaBaking powderSpices NutsPastaButterCheeseBreadMeat Vegetables FruitsWhat are some solids and liquids in kitchens ?When it comes to solids in the kitchen, we can mostly find either food ingredients, such as salt, flour, and spices, or actual food that can be prepared such as meat, vegetables, and bread.
As for liquids, these can be anything from drinks such as juice, water and wine, to liquids used for cooking such as oil, soy sauce and vinegar.
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Which algebraic expression is a polynomial term?
A polynomial term is an expression composed of constants, variables, and exponents.
A polynomial term is an expression composed of constants, variables, and exponents. Constants are the numerical values that don't change, while variables are values that can change. Exponents are numbers that indicate how many times a number is multiplied by itself. For example, 2^3 means 2 multiplied by itself 3 times, or 8. A polynomial term is an expression that combines constants, variables, and exponents, such as 6x^2 - 3x + 5. In this expression, 6, -3, and 5 are constants, x is a variable, and 2 and 1 are exponents. A polynomial term can also contain fractions, such as (2x + 1)/3. In this case, 2, 1, and 3 are constants, and x is a variable. Polynomial terms are the building blocks of polynomials, which are equations that consist of multiple polynomial terms.
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Need Help Find EI And ST
Answer:
Step-by-step explanation:
So first what you got to do is add and mulytplie
1 13. In the first few days of its life, the length of an earthworm I is thought to be proportional to the square root of the number of hours n which have elapsed since its birth. If a worm is 2 cm long after 1 hour, how long will it be after 4 hours? How long will it take to grow to a length of 14 cm?
The length of earthworm will be 4 cm after 4 hours. And the length is 14 cm after 49 hours.
What is meant by Proportion?Proportions are defined when two or more ratios are made to be equal to each other.
Two quantities are said to be directly proportional if a positive change in one quantity also lead to a positive change in the other quantity.
If a is proportional to b, we denote it as a ∝ b.
Given,
Length of an earthworm, l ∝ square root of the number of hours, n, which have elapsed since it's birth.
l ∝ √n
l = k √n, for some constant k.
If a worm is 2 cm long after 1 hour, we can write it as,
2 = k × √1
⇒ k = 2
So the proportionality constant is 2.
After 4 hours,
l = k √4
l = 2 × 2 = 4 cm
If the length is 14 cm,
14 = 2 √n
√n = 14 / 2
√n = 7
n = 7² = 49 hours
Hence the length of worm is 4 cm after 4 hours. It will take 49 hours to grow to a length of 14 cm.
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If the trapezoid below is reflected across the x-axis, what are the coordinates
of B?
Answer:
C
Step-by-step explanation:
under a reflection in the x- axis
a point (x, y ) → (x, - y ) , then
B (3, 8 ) → B' (3, - 8 )
Why greater than less than negative 2X squared +16 X -36
Answer:
Step-by-step explanation:
To determine whether a value is greater than or less than a specific result from an equation, you would need to substitute the value into the equation and solve for the result. For example, if you want to determine if the value "a" is greater than or less than the result of the equation -2x^2 + 16x - 36, you would substitute "a" for the variable x and solve for the result:
-2x^2 + 16x - 36 = -2a^2 + 16a - 36
Then you can compare the value of the result to "a" to determine whether it is greater than or less than.
If the result is greater than "a", you would write:
-2a^2 + 16a - 36 > a
If the result is less than "a", you would write:
-2a^2 + 16a - 36 < a
And if the result is equal to "a", you would write:
-2a^2 + 16a - 36 = a
It's important to note that the comparison only holds for a specific value of "a". The equation -2x^2 + 16x - 36 could have many solutions where the result is greater than, less than, or equal to "a".
Rewrite the expression in terms of ln 5 and ln 6.
ln(27000)
We can rewrite ln(27000) in terms of ln(5) and ln(6) as ln(27000) = 3ln(5) + 3ln(6) by using logarithmic property.
Why are logarithm qualities significant?Due of their connection to exponential functions, logarithmic functions are crucial. Logarithms can be used to examine exponential equations and the properties of exponential functions.
We can use the logarithmic property that says:
log_a(xⁿ) = n×log_a(x)
to break down 27000 into factors that involve 5 and 6.
First, we can write:
27000 = 5³× 6³
When we take the natural logarithm of both sides, we obtain:
ln(27000) = ln(5³ × 6³)
Using the property above, we can simplify this expression as:
ln(27000) = ln(5³) + ln(6³)
Using another logarithmic property that says:
log_a(bⁿ) = c×log_a(b)
we can further simplify the expression:
ln(27000) = 3ln(5) + 3ln(6)
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ZABC and ZQRS are supplementary angles.
If the measure of ZABC = 170°, what is the
measure of ZQRS?
m/QRS = ?
Answer:
[tex]10^{\circ}[/tex]
Step-by-step explanation:
Supplementary angles have measures that add to [tex]180^{\circ}[/tex].
A scuba diver dives 36 feet and
stops to look at a school of fish.
Then he dives down another 26 feet
How deep is the scuba diver now?
Answer:
62 Feet
Step-by-step explanation:
26+36=62
6 + 6 = 12
20 + 30 = 50
12 + 50 = 62
Answer:
The scuba diver is 62 feet deep.
Step-by-step explanation:
We know the scuba diver has dived 36 feet. When he stops to look at the school of fish, he doesn't dive down any further and stays at 36 feet. He then dives down another 26 feet
All we would need to do is add 36 and 26, which would give you your answer of 62.
Write an explicit formula for a_na n , the n^{\text{th}}n th term of the sequence 3, -15, 75, ...3,−15,75,....
The explicit formula for the geometric series is [tex]a_n = 3(5)^{n-1}[/tex].
What is geometric progression?A geometric series is one in which there is a constant separating the two succeeding numbers. In other words, to create a geometric progression, each succeeding term is multiplied by the constant term.
Given that the geometric sequence is,
3, 15, 75......
The common ratio of the series is calculated as the ratio of the second term to the first term,
r = 15 / 3
r = 5
The explicit formula can be written as:-
[tex]a_n = a_1(r)^{n-1}[/tex]
[tex]a_n = 3(5)^{n-1}[/tex]
Therefore, the formula is [tex]a_n = 3(5)^{n-1}[/tex].
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In stabilizing selection, what occurs in a population?a. The population shifts toward one of two extreme phenotypes.b. Both extreme phenotypes shift toward the middle.c. The intermediate phenotype becomes more common.d. The intermediate phenotype becomes rare.
In stabilizing selection, option (d) The intermediate phenotype becomes rare.
Stabilizing selection occurs when individuals with extreme phenotypes are at a disadvantage, and individuals with intermediate phenotypes have a greater chance of survival and reproduction.
This means that over time, the population shifts towards the intermediate phenotype. Let's take an example to explain this concept.
Suppose we have a population of rabbits with different fur colors, ranging from white to dark brown. Predators are more likely to spot white rabbits in a snowy environment, while brown rabbits are more likely to be seen in a forest environment. This means that the extreme phenotypes (white and dark brown) are at a disadvantage, while the intermediate phenotype (light brown) is more likely to survive and reproduce. Over time, the population will shift towards the light brown phenotype, as it is the most advantageous trait.
In conclusion, stabilizing selection is a mechanism of natural selection that promotes the preservation of the average characteristics of a population. It occurs when individuals with intermediate phenotypes have a higher chance of survival and reproduction, leading to the shift of the population towards the intermediate phenotype. Mathematically, we can represent this concept using the mean and standard deviation of a population.
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a Find: i the number of games played Goals 0 1 2 3 4 5 6 7 8
Frequency 6 11 5 11 4 0 2 0 1
ii the mode iii the median
iv the mean number of goals.
b Maha asked: ‘What is the average number of goals?’
Which would be the best average to use to answer this question? Give a reason for your answer.
1) The mean of the data is 4.45.
2) The mode of the data is 11.
3) The median of the data is 4.
What are the mean, mode, and median?The mean of the data is the ratio of the sum of the given data and the number of the count of the data.
The mode of the data is the number that is repeated maximum number of times. The median of the data is when the data is arranged in an increasing order then the middle most value will be the median of the data.
Given data is 6 11 5 11 4 0 2 0 1.
The mean of the data is,
Mean = ( 6 + 11 + 5 + 11 + 4 + 0 + 2 + 0 + 1 ) / 9
Mena = 4.45
Mode = 11
Median:- 0,0,1,2,4,5,6,11,11
Median = 4
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Madison took a taxi from her house to the airport. The taxi company charged a pick-up fee of $3.20 plus $5 per mile. The total fare was $98.20, not including the tip. Write and solve an equation which can be used to determine
m, the number of miles in the taxi ride.
Answer:
19 miles
Step-by-step explanation:
hope this helps!!
Someone please help with this question
A business owner wants to have the front window of her store painted and is considering two artists for the job. Mariana has quoted a flat rate of $135 for the job. Vincent's quote is $34 per hour, plus $67 to cover the cost of materials. Depending on how long it takes Vincent to paint the window, these two could end up charging the same amount. How much would it cost? How long would Vincent have to take?
Answer:
Step-by-step explanation:
Mariana's quote: 135
Vicent's quote: 34x+67
Say x=1, 34(1)+67=101
For 1 hour of Vincent's work it would be $101.
Say x=2. 34(2)+67=135
Vincent would have to work for two hours to charge the exact same as Mariana.
Example 7) Find three consecutive even integers such that the sum of the first and two times the
largest equals 20.
The consecutive even integers are 4,6 and 8.
What are the consecutive even integers?An even number is a number that can be perfectly divided by 2. An example of an even number is 10. A consecutive even number is an even number that follows each other on the number line.
Let the first even number be represented with x
The second even number : x + 2
The third even number : x + 4
x + 2(x + 4) = 20
x + 2x + 8 = 20
3x = 20 - 8
3x = 12
x = 12 / 3
x = 4
The second even number : 4 + 2 = 6
The third even number : 4 + 4 = 8
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Mary wants to hang a mirror in her room. The mirror and frame must have an area of 7 square feet. The mirror is 2 feet wide and 3 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?
x2 + 14x - 2 = 0
2x2 + 10x - 7 = 0
3x2 + 12x - 7 = 0
4x2 + 10x - 1 = 0
The correct quadratic equation that can be used to determine the thickness of the frame, x, is: 2x² + 10x - 7 = 0, Therefore Option B is the right answer
Here's how we can get this equation:
We are given that the mirror and frame together have an area of 7 square feet. The mirror itself has an area of 2 x 3 = 6 square feet. So, the area of the frame is 7 - 6 = 1 square foot.
Let's assume that the width of the frame is x feet. Then the overall width of the mirror and frame becomes 2 + 2x, and the overall length becomes 3 + 2x. The area of the mirror and frame can be expressed as:
(2 + 2x)(3 + 2x) = 6 + x(10 + 4x)
We know that this expression equals 7, so we can set it equal to 7 and obtain the quadratic equation:
2x² + 10x - 7 = 0
Therefore, the correct quadratic equation is 2x² + 10x - 7 = 0.
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Which of the following is NOT a characteristic of a plane?
The answer option which is not a characteristic of a plane include the following: C. thickness.
What is a plane?In Mathematics, a plane is sometimes referred to as a two-dimensional surface and it can be defined as a flat, two-dimensional surface with zero curvature and zero thickness, that extends indefinitely (infinitely). Additionally, two (2) planes intersect at a line.
What are the characteristics of a plane?Generally speaking, there are different characteristics of a plane and these include the following:
LengthFlat surface.Width.In this context, we can reasonably infer and logically deduce that thickness is not a characteristic of a plane.
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Complete Question:
Which of the following is NOT a characteristic of a plane?
A. length
B. flat surface
C. thickness
D. width
There are chairs from no. 27 to 66 in a row at an auditorium. How many chairs are there in a row
The number of chairs from number 27 to 66 in a row at an auditorium is calculated by using subtraction is 40.
To calculate the number of chairs in the row, we need to subtract the chair number of the first chair from the chair number of the last chair and add 1.
Number of chairs = (last chair number - first chair number) + 1
The first chair number is given as 27, and the last chair number is given as 66.
Substituting these values in the formula, we get:
Number of chairs = (66 - 27) + 1
Number of chairs = 40
Therefore, there are 40 chairs in the row, and the correct answer is option (3) 40.
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____ The given question is incorrect, the correct question is given below:
There are chairs from no, 27 to 66 in a row at an Auditorium. Then
how many chairs are there in the row ?
(1) 38
(2) 39
(3) 40
(4) 48
A person on a moving sidewalk travels 28 feet in 7 seconds. The moving sidewalk has a length of 200 feet. How long will it take to move from one end to the other?
It will take 50 seconds for the person to travel from one end to the other at the current speed.
How long will it take to move from one end to the other?
We know that the person travels 28 feet in 7 seconds, remember that speed is defined as the quotient between distance and time, then the person's speed is:
s = 28ft/7s = 4ft/s
Now we want to find the time T that it takes for the person to travel the 200 feet of the sidewalk, then we need to solve:
(4ft/s)*T = 200ft
T= 200ft/(4 ft/s) = 50s
It takes 50 seconds.
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Relative to a fixed origin O, the point A has position vector (2i + 3j - 4k), the point B has position vector (4i - 2j + 3k), and the point C has position vector (ai + 5j – 2k), where a is a constant and a < 0.
D is the point such that AB = BD.
(a) Find the position vector of D.
Given AC| = 4,
(b) find the value of a.
Answer: (a) To find the position vector of point D, we need to find the midpoint of the line segment AB. We can do this by taking the average of the position vectors of points A and B:
D = (A + B) / 2 = ((2i + 3j - 4k) + (4i - 2j + 3k)) / 2 = (3i + 0.5j - 0.5k)
So, the position vector of point D is (3i + 0.5j - 0.5k).
(b) To find the value of a, we use the fact that the distance between points A and C is 4. We can find the distance between two points by finding the magnitude of the difference between their position vectors. The position vector of point C is (ai + 5j – 2k), so the difference between the position vectors of points A and C is (ai + 5j – 2k) - (2i + 3j - 4k) = (a-2)i + 2j - (-2k).
The magnitude of this difference is given by:
|(ai + 5j - 2k) - (2i + 3j - 4k)| = √((a-2)^2 + 2^2 + 2^2) = 4
So, we have:
√((a-2)^2 + 2^2 + 2^2) = 4
(a-2)^2 + 2^2 + 2^2 = 16
(a-2)^2 = 16 - 4 - 4
(a-2)^2 = 8
a-2 = ±2√2
Since a < 0, we have:
a = 2 - 2√2
So, the value of a is 2 - 2√2.
Step-by-step explanation:
1. what is the last name of whom we honor for discovering ways to express and minimize logic though a new but similar form of algebra? 2. what does the k in k-map stand for? 3,4,5,
Boole. K-map stands for Karnaugh Map and is used to simplify and minimize the expression of logic in a similar form to algebra.
George Boole is the mathematician we honor for discovering ways to express and minimize logic through a new but similar form of algebra. The technique used to simplify and minimize these expressions is known as a Karnaugh Map, or K-map for short. A K-map is a visual representation of a Boolean expression using squares and circles to represent true or false variables in a table. By arranging the variables in the table, the same logic can be expressed in a simpler form with fewer variables. This allows for a simpler and more efficient form of logic expression. K-maps are used in many fields, such as digital logic design, where the efficiency of expression is important.
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Forty-two percent of what number is 168? Responses
40
70.6
400
705.6
Answer:
Your answer is: C) 400
Step-by-step explanation:
A right triangle has legs measuring 20 in. and 28 in. what is the length of the hypotenuse? round to the nearest tenth. responses 8.0 in. 8.0 in. 19.6 in. 19.6 in. 34.4 in. 34.4 in. 1184.0 in.
The length of the hypotenuse of a right triangle with legs measuring 20 inches and 28 inches is approximately 34.4 inches, found using the Pythagorean theorem.
The length of the hypotenuse of a right triangle with legs measuring 20 inches and 28 inches can be calculated using the Pythagorean theorem, which states that the square of the sum of the squares of the lengths of the legs determines the length of the hypotenuse.
So, if we call the length of the hypotenuse "h", we have [tex]h^{2}[/tex] = [tex]20^2 + 28^2[/tex]
Solving for h:
[tex]h^2 = 20^2 + 28^2[/tex]
[tex]h^2[/tex] = 400 + 784
[tex]h^2[/tex] = 1184
h = [tex]\sqrt{1184}[/tex]
h ≈ 34.4 in.
So, the length of the hypotenuse is approximately 34.4 inches, rounded to the nearest tenth.
The Pythagorean theorem is a fundamental mathematical relationship that states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal tothe squared lengths of the two legs added together. In this case, the two legs have lengths of 20 inches and 28 inches, and the length of the hypotenuse can be found by solving for the square root of the total of the leg squares.
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Anna ate 5/8 of an orange and gave the other 3/8 to her brother.
The difference between the amount Anna ate and the amount she gave to her brother can be found by subtracting 3/8 from 5/8. This can be expressed as an equation by writing 5/8 - 3/8 = x, where x is the difference.
5/8 - 3/8 = x
5/8 = 5 ÷ 8
= 0.625
3/8 = 3 ÷ 8
= 0.375
0.625 - 0.375 = x
= 0.25
Therefore, the difference between the amount Anna ate and the amount she gave to her brother is 0.25.The difference between the amount Anna ate and the amount she gave to her brother can be found by subtracting 3/8 from 5/8. This can be expressed as an equation by writing 5/8 - 3/8 = x, where x is the difference. To solve this equation, we first need to convert the fractions into decimal values. 5/8 is equal to 5 divided by 8, which is equal to 0.625. 3/8 is equal to 3 divided by 8, which is equal to 0.375. We can then subtract 0.375 from 0.625 to get the difference. This gives us 0.25, which is the difference between the amount Anna ate and the amount she gave to her brother. Therefore, the answer to the equation 5/8 - 3/8 = x is x = 0.25.
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The complete question is
Anna ate 5 8 of an orange and gave the other 3 8 to her brother. Which equation can be used to find the difference between the amount Anna ate and the amount she gave her brother?
5 Dans chaque cas, calculet une valeur approchée
au dixième près de la longueur, en cm, de chaque
cercle.
2.8 cm
18 m
J’ai besoin d’une réponse au plus vite possible
Compact fluorescent light (CFL) bulbs reduce energy waste. The amount of energy
waste that is reduced each day in a certain community can be estimated by -b² + 8b
where b is the number of bulbs. Divide by b to find the average amount of energy
saved per CFL bulb.
Transcribed image text: (1 point) Give an example of a matrix A and a vector b such that the solution set of Ax = b is a line in Rº that does not contain the origin. A= b
Matrix A is: A = [1 2 3] and Matrix B is: B = [1]
[2 4 6] [2]
[1 1 1] [3]
An example of a 3x3 matrix A and a 3x1 matrix B such that the solution set of Ax = b is a line in R³ that does not contain the origin:
A = [1 2 3]
[2 4 6]
[1 1 1]
B = [1]
[2]
[3]
To check that the solution set of Ax = b is a line in R³, we can solve for x in terms of a parameter t:
Ax = b
[1 2 3] [x1] = [1]
[2 4 6] [x2] [2]
[1 1 1] [x3] [3]
Ax = b
x1 + 2x2 + 3x3 = 1
2x1 + 4x2 + 6x3 = 2
x1 + x2 + x3 = 3
Dividing the second equation by 2 and subtracting it from the first equation, we get:
-x1 - x2 = -1
Solving for x2 in terms of x1 and x3, we get:
x2 = -x1 + 1 - (3/2)x3
Solving for x3 in terms of a parameter t, we get:
x3 = t
Then, x1 can be expressed in terms of t as:
x1 = -t + 1
Therefore, the solution set of Ax = b is:
x = [-t + 1]
[-t + 1 - (3/2)t]
[t]
which is a line passing through the point (1, 1/2, 0) with a direction vector [-1, -3/2, 1].
A × [0; 0; 0] = [0; 0; 0]
Therefore, the origin is not on the line of solutions.
So, Matrix A is:
A = [1 2 3]
[2 4 6]
[1 1 1]
and Matrix B is:
B = [1]
[2]
[3]
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Ben says this system of equations has one solution. Is he correct? Explain
Answer:
what system of equations? and ben is a bad name, try and come up with another one
Step-by-step explanation:
Graph the line with Slope 7 and y-intercept -8
Answer:
y=7x-8
Step-by-step explanation:
You start off with the equation y= mx+b, where m = the slope (7/1) and b, which is (0,-8). Then you can graph. You first put a dot at (0,-8). Then you count up to 7 and then go to the right 1. You continue the pattern until the line is over the graph. The equation would be y= 7x-8
