We need to round up to the next full number because we are unable to equation have a fraction of a boat. The organization will thus require 157 boats to hold the entire 1,254 persons.
What is equation?Using the equals symbol (=) to indicate equivalence, a math equation links two statements. Algebraic equations prove the equality of two mathematical expressions by a mathematical assertion. The equal sign, for example, provides a gap between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. You can use a mathematical formula to understand the connection between the two phrases that are written on opposite sides of a letter. Most of the time, the logo and the particular software match. e.g., 2x - 4 = 2 is an example.
We may divide the total number of persons by the capacity of each boat to determine the number of boats required to hold a party of 1,254 individuals:
8 individuals per boat times 1,254 passengers is 156.75 boats.
We need to round up to the next full number because we are unable to have a fraction of a boat. The organization will thus require 157 boats to hold the entire 1,254 persons.
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20 POINTSS!! HURRY!
Airplane A traveled 1662 miles in six hours.
For Airplane B, y =
922/
3
x represents its rate of speed over the same six hours.
Compare the two airplanes to determine which airplane traveled at a faster rate?
Group of answer choices
Airplane A
Airplane B
airplane A
To compare the rate of speed of Airplane A and Airplane B, we need to calculate the speed of Airplane B first.
The formula to calculate distance is:
distance = rate x time
For Airplane A, we know:
distance = 1662 miles
time = 6 hours
So, we can rearrange the formula to solve for the rate:
rate = distance / time = 1662 / 6 = 277 miles per hour
For Airplane B, we know:
y = 922/3
x = rate of speed over 6 hours
We can use the formula to solve for x:
distance = rate x time
922/3 = x * 6
x = (922/3) / 6 = 153.67 miles per hour
Comparing the rates of the two airplanes, we can see that Airplane A traveled at a faster rate with 277 miles per hour compared to Airplane B's rate of 153.67 miles per hour. Therefore, Airplane A traveled at a faster rate.
Which statement is true about evaluating the expression 72÷12+9−5 on the basic calcul
On simplifying the given expression using simplification method BODMAS, we get the answer 10. Thus, in the calculator the calculation must be done from left to right.
What is simplification in mathematics?Simplification means using various operations to reduce the formula to a simpler form, and approximation simplifies the formula to the nearest, but not exactly correct, value.
What is BODMAS?BODMAS in simplification stands for Bracket, Ob, Division, Multiplication, Addition, and Subtraction. BODMAS is used to describe the order of operations in formulas. In some areas, BODMAS is also known as PEDMAS. This represents parentheses, exponents, division, multiplication, addition, and subtraction.
Solution using BODMAS and simplifying it:
72÷12+9−5 = (72/12) + 9 - 5
=6 + 9 - 5
= 15 - 5
⇒72÷12+9−5 = 10
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Emilia's lemon cookie recipe calls for 1 1/8 cups of sugar. How much sugar would Emilia use to make 3 5/6 batches of cookies?
To find how much sugar would Emilia use to make about 3 5/6 batches of cookies.
1 1/8 cups of sugar
Next, we need to convert the mixed number to an improper fraction:
1 1/8 = (8 + 1) / 8 = 9/8
So, the amount of sugar needed for one batch of cookies is:
9/8 cups of sugar
To find the total amount of sugar needed for 3 5/6 batches, we can multiply the amount of sugar per batch by the number of batches:
(9/8 cups of sugar) x (23/6 batches) = 69/48 cups of sugar
thus, Emilia would need 69/48 cups of sugar to make 3 5/6 batches of cookies.
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At this Sunday’s Super Bowl game, 150 out of thefirst 500 people who entered the main gate were not wearing team jerseys. Ifthis sample is representative of the 75,000 people attending the game, abouthow many of them will probably NOT be wearing team jerseys? 2,500 people 25,000 people 22,500 people 2,200 people
As a result, approximately 22,500 spectators at the Super Bowl will likely not be donning club jerseys. The correct response is (C) 22,500 people.
what is proportionality ?A mathematical concept known as proportionality describes the relationship between two quantities that change in a way that keeps their ratio constant. This means that if the size of one quantity increases or decreases by a certain amount, the size of the other quantity will do the same, maintaining their relative size. In other words, we can state that A is directly proportional to B if we have two quantities, A and B, and their ratio is constant. Frequently, this is expressed as: A ∝ B or A = k * B where k is a ratio constant.
given
The number of spectators who won't be sporting team jerseys at the Super Bowl can be estimated using proportions:
If 150 out of the first 500 individuals to enter through the main gate were not donning team uniforms, then the percentage of those without team uniforms is:
150/500 = 0.3
This indicates that 30% of those who entered through the main gate did not have team jerseys on.
We can determine the approximate number of spectators who won't be donning team jerseys as follows, assuming that this proportion is representative of the entire 75,000 people in attendance:
0.3 * 75,000 = 22,500
As a result, approximately 22,500 spectators at the Super Bowl will likely not be donning club jerseys. The correct response is (C) 22,500 people.
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Need help with these questions please
1. The height of the pyramid is 3.7 inches.
2. The length of the crossbar is 2√2 feet.
What is a pyramid?A three-dimensional figure is a pyramid. Its base is a flat polygon. The remaining faces are all triangles and are referred to as lateral faces. The number of sides on its base is equal to the number of lateral faces. The line segments that two faces intersect to form its edges. The intersection of three or more edges forms a vertex.
1. We know, The height, slant height, and half of the base length form a
right-angled triangle
Therefore, h² = 4² - (3/2)².
h² = 13.75
h = 3.7 inches.
2. We know, In a 45°, 45° and 90° triangle, It is an isosceles right-angled triangle, The hypotenuse is √2 times the two similar sides.
Therefore, From the given information, The length of the crossbar is
2√2 feet.
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y>=-(7)/(6)x Alot points on the Boundary Ine. Select the Ene to swith between solif and dotted. Select a reglon to shade it.
The final solution to the inequality y>=-(7)/(6)x is the shaded region on the graph.
To solve the inequality y>=-(7)/(6)x, we will first graph the boundary line and then shade the appropriate region.
1. Begin by graphing the boundary line y=-(7)/(6)x. This line has a slope of -(7)/(6) and passes through the origin (0,0).
2. Since the inequality includes the "greater than or equal to" symbol (>=), the boundary line should be solid to indicate that points on the line are included in the solution.
3. Next, we need to determine which region to shade. To do this, we can choose a test point that is not on the boundary line. A common test point is (0,1), which is above the boundary line.
4. Substitute the coordinates of the test point into the inequality to see if it is true or false: 1>=-(7)/(6)(0)
5. Since the inequality is true, the region that includes the test point is the solution. This means we should shade the region above the boundary line.
6. The final graph should have a solid boundary line with the region above it shaded.
The solution to the inequality y>=-(7)/(6)x is the shaded region on the graph.
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The mean selling price of new homes was $114,000. The population standard deviation was $5,000. A random sample of 100 new home sales was taken without doing the calculations, state in which of the following ranges the sample mean selling price is most likely to lie? a. $115,000 - $117,000 b. $116,000 - $118,000 c. $113,000 - $115,000 d. $114,000 -- $116,000
The mean selling price of new homes was $114,000. The population standard deviation was $5,000. A random sample of 100 new home sales was taken without doing the calculations, ranges the sample mean selling price is most likely to lie between C) $113,000 - $115,000.
The sample mean selling price is most likely to lie in the range of $113,000 to $115,000 because this range is within one standard deviation (i.e., $5,000) of the population mean of $114,000, and therefore it contains approximately 68% of the sample mean values. The other ranges are outside one standard deviation from the mean, and therefore, the probability of the sample mean being in those ranges is lower. However, it is important to note that the actual sample mean could fall outside this range as it is still subject to random variation.
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need help with this question
The amount of element left after the decay is found as 43 grams.
Explain about the element's decay rate?The proportion of radioactive nuclei that decrease per unit of time is the rate of decay, or radioactivity, of a measurement of a radioactive substance. The amount of time needed for the substrate concentration to drop to half its initial value is known as the half-life of a reaction. One element spontaneously changes into another during radioactive decay. Only by altering the amount of protons within the nucleus is this possible.Decay rate is given as:
N = N₀(1 - r)ˣ
x - is the time in minutes
N₀ - initial mass (570 grams)
r - rate of decay (18%)
Put the values:
N = 570(1 - 0.18)¹³
N = 570*0.0757
N = 43
Thus, the amount of element left after the decay is found as 43 grams.
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Im confused of what the answer should be
The population of bears in a national forest is changing according to the function N(t) = 850(0.96)*, where t is the time in years and N(C) is the number of bears.
Which statement explains how the bear population is changing?
A. The population is decreasing by 4% per year.
B. The population is increasing by 96% per year.
C. The population is increasing by 4% per year.
D. The population is decreasing by 96% per year.
The population function is N(t) = 850(0.96)^t.
The base of the exponential function is (0.96), which is less than 1. This means that the function is decreasing over time.
Therefore, the correct answer is:
A. The population is decreasing by 4% per year.
Dierks made $13.50 per hour. He got a new job in which he made 8% more. How much did her her make per hour at his new job?
Answer: $14.58
Step-by-step explanation:
13.50 x .08 = 1.08
13.50 + 1.08 = 14.58
How much distance will a tein cover in 3⅓ hoursif it maintains a constant speed of 80¼ km/h?
Enter the zero element (zero vector) for each vector space. Use the following syntax to enter your answers. Enter the vector⟨1,2,3⟩using⟨1,2,3⟩. Enter the matrix[1324]using[[1,2],[3,4]]. Enter the functionf(x)=x2−sin(x)usingf(x)=x−2−sin(x), including the partf(x)=. 1. The zero vector of the vector spaceR2is 2. The zero vector of the vector space of2×2matrices is 3. The zero vector for the vector space of all functionsf:R→Ris
1) The zero vector of the vector space R2 is ⟨0,0⟩.
2) The zero vector of the vector space of 2×2 matrices is [[0,0],[0,0]].
3) The zero vector for the vector space of all functions f:R→R is f(x) = 0.
What is vector space?
A vector space is a mathematical structure consisting of a set of vectors that can be added together and scaled (multiplied) by scalars, such as real numbers, satisfying certain axioms.
The zero vector of the vector space R2 is ⟨0, 0⟩. This is because the zero vector of a vector space is the unique vector which when added to any vector in the space results in that same vector. In R2, the vector ⟨0, 0⟩ has this property, because for any vector ⟨a, b⟩ in R2, ⟨0, 0⟩ + ⟨a, b⟩ = ⟨a, b⟩.
The zero vector of the vector space of 2×2 matrices is [[0,0],[0,0]]. This is because the zero vector of a vector space is the unique matrix which when added to any matrix in the space results in that same matrix. In the space of 2×2 matrices, the matrix [[0,0],[0,0]] has this property, because for any matrix [[a,b],[c,d]] in the space, [[0,0],[0,0]] + [[a,b],[c,d]] = [[a,b],[c,d]].
The zero vector for the vector space of all functions f:R→R is f(x) = 0. This is because the zero vector of a vector space is the unique function which when added to any function in the space results in that same function. In the space of all functions f:R→R, the function f(x) = 0 has this property, because for any function f(x), f(x) + 0 = f(x).
Hence,
1) The zero vector of the vector space R2 is ⟨0,0⟩.
2) The zero vector of the vector space of 2×2 matrices is [[0,0],[0,0]].
3) The zero vector for the vector space of all functions f:R→R is f(x) = 0.
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Given the information, please find the simple multiplier in the economy:
AD: y = 710 -30p + 5g
AS: y = 10 + 5p - 2s
g is government purchases, and s is the world price of some commodity.
Please explain how to do this, I don't need the answer unless I have the steps
The simple multiplier of the economy represented by the system of equation above is: 4/7.
What is Simple Multiplier?
The simple multiplier is the ratio of the change in equilibrium output to a change in autonomous expenditures, such as government spending or investment.
To find the simple multiplier in the economy, we need to first determine the equation for equilibrium output, which is where aggregate demand (AD) equals aggregate supply (AS).
Setting y in both equations equal to each other, we get:
710 - 30p + 5g = 10 + 5p - 2s
Simplifying and rearranging, we get:
35p = 700 + 2s - 5g
p = (20/7) + (2/35)s - (1/7)g
Now that we have the equilibrium price, we can substitute it back into the AD equation to find the equilibrium output (y):
y = 710 - 30[(20/7) + (2/35)s - (1/7)g] + 5g
y = (400/7) + (6/7)s + (4/7)g
The simple multiplier is then equal to the change in equilibrium output divided by the change in government purchases:
simple multiplier = Δy/Δg = 4/7
Therefore, the simple multiplier in the economy is 4/7.
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Write an equation for the graph that passes through (0,9) and has a slope of -3.
The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. We are given that the line passes through the point (0,9) and has a slope of -3, so we can substitute these values into the equation to find the y-intercept:
y = mx + b
9 = (-3)(0) + b
b = 9
Now we know that the y-intercept is 9, so we can write the equation of the line:
y = -3x + 9
Therefore, the equation of the graph that passes through (0,9) and has a slope of -3 is y = -3x + 9.
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Plot the points A(-2,-3), B(1, 12), C(3, -4) on the coordinate axes below. State the
coordinates of point D such that A, B, C, and D would form a rectangle. (Plotting
point D is optional.)
The opposite sides of the quadrilateral should be parallel and the diagonals should be equal. [For a rectangle]
First, let's find the slope of AB and its perpendicular slope.
Slope of AB = (y2 - y1)/(x2 - x1) = (12 - (-3))/(1 - (-2)) = 5
Perpendicular slope of AB = -1/5
The midpoint of AB is ((-2+1)/2, (-3+12)/2) = (-0.5, 4.5)
Let D be the point on line segment AC such that AD is perpendicular to AC. Since AB is parallel to DC, the slope of DC is also 5.
Slope of AC = (-4 - (-3))/(3 - (-2)) = -1/5
The equation of line AC is y = (-1/5)x - (13/5)
The equation of line DC passing through (3,-4) with slope 5 is y - (-4) = 5(x - 3)
Solving these two equations, we get D(2,-14/5).
Therefore, the coordinates of point D are (2, -14/5).
We can plot the points on the coordinate axes and verify that A, B, C, and D indeed form a rectangle.
Find the volume of the earth dug out from a pit 6. 5 m long 2. 4 M wide and 1. 5 m deep
The volume of the earth dug out from a pit = 23.4 m³
Let us assume that l represents the length of the pit, 'w' represents the width and 'h' be the height of the pit.
Here, the length of the pit(l) = 6.5 m
the width of the pit (w) = 2.4 m
height of the pit(h) = 1.5 m
We need to find the volume of earth dug out from a pit.
We know that pit is of the cuboid shape.
Using the formula of volume of cuboid,
V = l × w × h
V = 6.5 × 2.4 × 1.5
V = 23.4 m³
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7 divided by 1 and three thirds
Answer: 2.1429
Step-by-step explanation:
The answer is 2.1429. This is because 7 divided by 1 is 7, and 7 divided by three thirds is the same as 7 divided by 1.5, which is equal to 4.6666. Therefore, 7 divided by 1 and three thirds is equal to 7 divided by 4.6666, which equals 2.1429.
If the principal is 18000 the time is 54 months and the simple interest is 4252.50 what is the interest rate
Answer:
To find the interest rate when given the principal, time, and simple interest, we can use the formula:
Simple Interest = (Principal * Rate * Time) / 100
where:
Simple Interest is the given value of 4252.50
Principal is 18000
Time is 54 months
Rate is the unknown we want to solve for
Substituting the given values, we get:
4252.50 = (18000 * Rate * 54) / 100
Multiplying both sides by 100 and dividing by 18000 * 54, we get:
Rate = (4252.50 * 100) / (18000 * 54)
Rate = 4.398%
Therefore, the interest rate is 4.398% (rounded to three decimal places).
Step-by-step explanation:
Sure! Here is a step-by-step explanation of how to find the interest rate:
Given:
Principal = 18000
Time = 54 months
Simple Interest = 4252.50
Formula:
Simple Interest = (Principal * Rate * Time) / 100
We want to solve for Rate.
Substitute the given values into the formula:
4252.50 = (18000 * Rate * 54) / 100
Simplify by multiplying both sides by 100:
425250 = 18000 * Rate * 54
Divide both sides by 18000 * 54:
Rate = 425250 / (18000 * 54)
Simplify the expression on the right-hand side:
Rate = 0.04398
Convert the decimal to a percentage:
Rate = 4.398%
Therefore, the interest rate is 4.398%.
Using the formula for simple interest, the value for interest rate is obtained as 5.25%.
What is Simple Interest?
Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.
We can use the formula for simple interest -
I = P × r × t
where I is the interest, P is the principal, r is the interest rate, and t is the time in years.
In this case, the principal is $18,000, the time is 54 months which is 4.5 years, and the simple interest is $4,252.50.
Substituting these values in the formula, we get:
4252.50 = 18000 × r × 4.5
Solving for r, we get -
r = 4252.50 / (18000 × 4.5)
= 0.0525 or 5.25%
Therefore, the interest rate is 5.25%.
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For the following decision problem where the objective is to maximize the expected return, find a. The optimal policy and expected return. b. The value of knowing X, but not Y, before D. c. The value of knowing Y, but not X, before D. d. The value of knowing both X and Y before D. e. Draw the influence diagram that corresponds to this decision tree.
a. The optimal policy and expected return can be found by working backwards from the end nodes of the decision tree. For each decision node, choose the action that results in the highest expected return. The expected return is calculated by multiplying the probability of each outcome by the corresponding return and summing the results. The optimal policy is to choose A if X is high, and B if X is low.
The expected return is 0.7*30 + 0.3*10 = 24.
b. The value of knowing X, but not Y, before D is calculated by subtracting the expected return without knowing X from the expected return with knowing X.
The expected return without knowing X is 0.5*24 + 0.5*24 = 24.
The expected return with knowing X is 0.7*30 + 0.3*10 = 24.
Therefore, the value of knowing X is 24 - 24 = 0.
c. The value of knowing Y, but not X, before D is calculated by subtracting the expected return without knowing Y from the expected return with knowing Y.
The expected return without knowing Y is 0.5*24 + 0.5*24 = 24.
The expected return with knowing Y is 0.8*30 + 0.2*10 = 26.
Therefore, the value of knowing Y is 26 - 24 = 2.
d. The value of knowing both X and Y before D is calculated by subtracting the expected return without knowing X or Y from the expected return with knowing both X and Y.
The expected return without knowing X or Y is 0.5*24 + 0.5*24 = 24.
The expected return with knowing both X and Y is 0.7*0.8*30 + 0.7*0.2*10 + 0.3*0.8*10 + 0.3*0.2*30 = 25.2.
Therefore, the value of knowing both X and Y is 25.2 - 24 = 1.2.
e. The influence diagram that corresponds to this decision tree is shown below:
X -> D -> Y -> R
-> A -> R
-> B -> R
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Michael sang 12 songs. Every song was 3/8 minutes long. For how much time did he sing in total? Write your answer in simplest form.
Answer:
Total time = (length of one song) x (number of songs)
Length of one song = 3/8 minutes
Number of songs = 12
Total time = (3/8) x 12
Total time = 36/8
Simplifying the fraction, we get:
Total time = 4 and 4/8 minutes
Total time = 4 and 1/2 minutes
Therefore, Michael sang for a total of 4 and 1/2 minutes.
We are working with exponential and logarithmic equations.
Your goal is to write an equation with exactly one real solution
and
Make it solvable with paper and pencil.
Be creative!
When working with exponential and logarithmic equations, there are several ways to create an equation with exactly one real solution. One way is to use the properties of logarithms to create an equation that can be solved using paper and pencil. Here is an example:
Let's start with the equation y = 2ˣ. This is an exponential equation, and we want to find the value of x that makes the equation true. To do this, we can use the property of logarithms that states log_b(a) = n if and only if bⁿ = a. This means that we can rewrite the equation as log_2(y) = x.
Now, let's make the equation more interesting by adding a constant to both sides. We'll add 3 to the left side and 2 to the right side, giving us the equation log_2(y) + 3 = x + 2.
Finally, let's rearrange the equation so that we have a logarithmic equation with one real solution. We'll subtract 2 from both sides and then subtract x from both sides, giving us the equation log_2(y) - x + 1 = 0.
This equation has exactly one real solution, and it can be solved using paper and pencil. One way to solve it is to use the properties of logarithms to rewrite the equation in terms of y and then solve for y. Another way is to graph both sides of the equation and find the point where they intersect.
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From the sum of 2x –2 y - 24 and 2 y + 24, subtract -4x –2 y + 12
The final expression after the subtraction is -6x + 4y + 12.
The given expression is:
(2x - 2y - 24 + 2y + 24) - (-4x - 2y + 12)
Simplifying the expression inside the parentheses, we get:
2x - 2y + 2y + 24 - 4x + 2y - 12
Combining like terms, we get:
(-2x + 2y + 2y) + (24 - 12) - 4x
Simplifying further, we get:
-2x + 4y + 12 - 4x
Combining like terms, we get:
-6x + 4y + 12
Therefore, the final expression after the subtraction is -6x + 4y + 12.
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A golf store pays its wholesaler $40 for a certain club. and then sells it to a golfer for $75. What is the markup rate?
Answer:
87.5% increase
Step-by-step explanation:
75 - 40 = 35
Find what percentage 35 is of 40, and you can do so by dividing.
35 ÷ 40 = 0.875
0.875 = 87.5%
A=20 and b=15 what is the value of cos0?
Answer:
Step-by-step explanation:
Use Pythagorean's Theorem to find the length of the hypotenuse
a² + b² = c²
20² + 15² = c²
400 + 225 = c²
625 = c²
25 = c
Cosine is adjacent over hypotenuse, so
20/25 = 4/5
If h(x) = (-x + 1)2 – 5 and g(x) = -x – 2, then (hog)(x) = ___ ? A. -73 + 8x + 8 I B. -x2 + 2x + 2 C. -22 D. -22 +61 +4 E. 12 + 6x +4 32.
If h(x) = (-x + 1)2 – 5 and g(x) = -x – 2, then (hog)(x) will be B. -x2 + 2x + 2.
If h(x) = (-x + 1)2 – 5 and g(x) = -x – 2, then (hog)(x) = (h(g(x)). This means that we need to plug in the value of g(x) into the equation for h(x) and simplify. To get this result, first use the chain rule:
(hog)(x) = h(g(x)).
So, (hog)(x) = h(g(x)) = h(-x-2) = (-(x)-2+1)2 – 5 = (-x-1)2 – 5
Expanding the square, we get:
(hog)(x) = (-x-1)(-x-1) – 5 = x2 + 2x + 1 – 5 = x2 + 2x - 4
Therefore, the correct answer is B. -x2 + 2x + 2.
Answer: B. -x2 + 2x + 2
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p please help I have no clue.
Answer:
11 meters, 4.1 centimeters
Step-by-step explanation:
If for every centimeter it equals 2 meters, we can use this expression to solve for the width of the building in real-life:
5.5 × 2 = 11Therefore, the width of the building is 11 meters in real life.
If the real-life height of the building is 8.2 m tall, then we can use this expression:
8.2 ÷ 2 = 4.1We multiplied the first time, so why are we dividing now?Because we were given the drawings width the first time, we needed to multiply by 2 to get the real-life height in meters. But now that we are given the real-life height, we now need to divide by 2 to get the height of the drawing in centimeters.
Therefore, the width, in meters, of the building in real life is 11 meters, and the height of the drawing is 4.1 centimeters.
Solve the system by Elimination.
−6x+2y=−28
−4x+5y=18
(-8, -6)
(8, 6)
(8, 10)
(8, 5)
Answer:
x would be 8 and y is 10
so (8,10)
Step-by-step explanation:
hope it helps
Write the vector form of the general solution of the given system of linear equations. X1+x2+x4 = 0
X1 +2x2 +4x4 = 0
2x1 -4x4 = 0
The vector form of the general solution of the given system of linear equations is given by:
{x} = {x1, x2, x4} = s { -1, 1, 0} + t { -2, 0, 1}
where s and t are arbitrary constants.
To find the vector form of the general solution, we need to find the null space of the coefficient matrix of the system of linear equations. The coefficient matrix of the system is:
A = [ 1 1 0 1; 1 2 0 4; 2 0 0 -4]
The null space of A is the set of all vectors x such that Ax = 0. We can find the null space of A by reducing A to its reduced row echelon form:
A = [ 1 0 0 -2; 0 1 0 1; 0 0 0 0]
From the reduced row echelon form of A, we can see that x1 and x2 are the leading variables and x4 is the free variable. Therefore, the general solution of the system of linear equations is given by:
x1 = -2x4
x2 = x4
x4 = x4
We can write the general solution in vector form as:
{x} = {x1, x2, x4} = x4 { -2, 1, 1}
Since x4 is an arbitrary constant, we can write the general solution in terms of two arbitrary constants s and t as:
{x} = {x1, x2, x4} = s { -1, 1, 0} + t { -2, 0, 1}
Therefore, the vector form of the general solution of the given system of linear equations is:
{x} = {x1, x2, x4} = s { -1, 1, 0} + t { -2, 0, 1}
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Identify the transformations that have been applied to the parent function y=-(1)/(2)(x-3)^(2)-5. Select all that apply.
The transformations that have been applied to the parent function y=-(1)/(2)(x-3)^(2)-5 are: horizontal shift, vertical shift, and vertical stretch.
The transformations that have been applied to the parent function y=-(1)/(2)(x-3)^(2)-5 are:
- Horizontal shift: The parent function has been shifted to the right by 3 units. This is indicated by the subtraction of 3 from x in the equation.
- Vertical shift: The parent function has been shifted downward by 5 units. This is indicated by the subtraction of 5 from the entire equation.
- Vertical stretch: The parent function has been stretched vertically by a factor of (1)/(2). This is indicated by the multiplication of the entire equation by (1)/(2).
Therefore, the correct answers are horizontal shift, vertical shift, and vertical stretch.
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