Answer:
1 mile is equal to 1,760 yards. Therefore, 3 miles is equal to 3 x 1,760 = 5,280 yards.
Comparing 5,280 yards to 1,000 yards, we can see that 5,280 yards is greater than 1,000 yards.
To determine how much greater, we can subtract 1,000 from 5,280:
5,280 - 1,000 = 4,280
Therefore, 3 miles is 4,280 yards greater than 1,000 yards.
Compare the numbers 144 and 12. 9329....
Select from the drop-down menu to correctly complete the statement.
√144 is
is Choose... v 12.9329...
Two comparations can be done:
√144 is rational and 12.9329... is irrational.12.9329...> √144 How to compare the two numbers?I understand that we want to compare the numbers:
√144 and 12.9329...
Notice that the second number has infinite decimals after the decimal point (and there is no a clear pattern), so it is an irrational number.
For the first one, we know that:
12*12 = 144
So 144 is a perfect square, then when we apply the square root we will get:
√144 = 12
Then the two comparations are:
√144 is rational and 12.9329... is irrational.
And:
12.9329...> √144
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Solve for x. Assume that lines which appear to be diameters are actual diameters.
Assuming the lines, which appear to be diameters, are actual diameters. The value of x is 10.63.
What is the diameter?Any straight line that connects two points on a circle's circumference and goes through the circle's center. The length of such a line in geometry. The greatest separation possible between any two points in a metric space (geometry).
Exterior angles are 128, 32, and 45
Interior angles are 11x+4 and 85
Exterior angles = interior angles
128 + 32 + 45 = 11x+4 + 85
205 = 11x + 88
11x = 205 - 88 = 117
x = 117/11
x = 10.63
Therefore, the value of x is 10.63.
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Please Help! I don't understand.
Answer:
36πmm^2
Step-by-step explanation:
6mm^2=36mm
36mm×π=36πmm^2
Visual domain and range
Determine the range of the following graph
Answer:
[-4, 2]
Step-by-step explanation:
You want the range of the graph shown.
RangeThe range is the vertical extent of the graph. This graph has a minimum at y=-4 and a maximum of y=2. All values between these are represented, so the range is ...
[-4, 2] . . . . or -4 ≤ y ≤ 2
x=1/2 and y= -5
4(1/2) (4) -3 (-5)
The value of 4x - 3y when x=1/2 and y=-5 is -13. The given equation can be simplified by using the distributive property.
What is an equation?An mathematical equation is a statement that states that two expressions are equal. It is usually written using symbols such as +, -, x, and ÷. They can be used to find unknown values, such as the area of a circle or the speed of a moving object.
The equation 4x - 3y = 0 can be rearranged to 4x = 3y. We can substitute 1/2 for x and -5 for y to determine the value of the equation. The equation becomes 4(1/2) (4) -3 (-5). This equation can be simplified by using the distributive property. The equation simplifies to 4/2 - 15. 4/2 simplifies to 2 and -15 simplifies to -15. The final answer is 2 - 15 = -13.
Therefore, the value of 4x - 3y when x=1/2 and y=-5 is -13.
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The value of 4x - 3y when x=1/2 and y=-5 is -13. The given equation can be simplified by using the distributive property.
What is an equation?An mathematical equation is a statement that states that two expressions are equal. It is usually written using symbols such as +, -, x, and ÷. They can be used to find unknown values, such as the area of a circle or the speed of a moving object.
The equation 4x - 3y = 0 can be rearranged to 4x = 3y. We can substitute 1/2 for x and -5 for y to determine the value of the equation. The equation becomes 4(1/2) (4) -3 (-5). This equation can be simplified by using the distributive property. The equation simplifies to 4/2 - 15. 4/2 simplifies to 2 and -15 simplifies to -15. The final answer is 2 - 15 = -13.
Therefore, the value of 4x - 3y when x=1/2 and y=-5 is -13.
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Complete question -
Find the value of 4x - 3y when x=1/2 and y=-5.
1. After watching "Nike an Example of a TNC (Transnational Corporation)" and reviewing your readings and notes, what is the effect of Nike's production of shoes and clothing around the world has on the standard of living of workers in the countries where is produces ("the global South") and in the countries where it sells its products ("the global North")?
After watching "Nike an Example of a TNC (Transnational Corporation)" and reviewing the readings and notes, it is clear that Nike's production of shoes and clothing around the world has had a significant effect on the standard of living of workers in the countries where it produces ("the global South") and in the countries where it sells its products ("the global North").
In the global South, Nike's production has led to the creation of jobs and an increase in income for workers. However, these workers often face poor working conditions and low wages, which can negatively impact their standard of living. Additionally, the environmental impact of Nike's production can also have a negative effect on the standard of living for workers and their communities.
In the global North, Nike's production has led to the availability of affordable and fashionable clothing and shoes. However, the low prices of these products are often achieved through the exploitation of workers in the global South, which can lead to ethical concerns for consumers. Additionally, the environmental impact of Nike's production can also have a negative effect on the standard of living for consumers and their communities.
Overall, Nike's production of shoes and clothing around the world has had a significant effect on the standard of living of workers in the global South and consumers in the global North. While there are some benefits, such as job creation and affordable products, there are also significant negative impacts, including poor working conditions, low wages, and environmental degradation.
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To determine the number of squirrels in a conservation area, a researcher catches and marks squirrels. Then the researcher releases them. Later squirrels are caught and it is found that of them are tagged. About how many squirrels are in the conservation area?
Therefore , the solution of the given problem of unitary method comes out to be t there are 1000 squirrels in the conservation area.
Unitary method: what is it?To finish a job using the unitary method, divide the lengths of just this minute subset by two. In a nutshell, the unit method eliminates a desired item from both the characterized by a set and colour subsets. 40 pens, for instance, variable will cost Rupees ($1.01). It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait.
Here,
The Lincoln-Petersen index can be used to calculate an approximate squirrel population estimate for the protected area:
There were n1 squirrels in the first group.
Second sample's fox count is equal to n2.
Second sample's total number of labelled squirrels is m2.
The following provides the Lincoln-Petersen index:
=> n1 * n2 / m2
Assume that the first sample consisted of 100 squirrels that were captured and tagged by the researcher. 20 of the 200 squirrels the researcher caught for the second group had tags on them. the following algorithm is used.
=> n1 * n2 / m2 = 100 * 200 / 20 = 1000
Therefore, it is believed that there are 1000 squirrels in the conservation area. It is crucial to keep in mind that this is only an approximation and might not be correct.
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Problem 2
Let A= [ 9 2 -22]
[ 0 -2 0 ]
[ 1 0 -4 ]
a) find the characteristic polynomial of A
b) Find the two eigenvalues of A
(c) Find a basis for the eigenspace corresponding to the smallest eigenvalue. (d) Find a basis for the eigenspace corresponding to the largest eigenvalue.
{-2 2 22}
a) The characteristic polynomial of A is given by:
$$p_A(\lambda) = \lambda^3 - 5\lambda^2 + 18\lambda + 36$$
b) The two eigenvalues of A are:
$$\lambda_1=2, \lambda_2=-4, \lambda_3=9$$
c) A basis for the eigenspace corresponding to the smallest eigenvalue $\lambda_2=-4$ is given by the set of vectors:
$$\begin{bmatrix} 0\\1\\0 \end{bmatrix}, \begin{bmatrix} 2\\0\\1 \end{bmatrix}$$
d) A basis for the eigenspace corresponding to the largest eigenvalue $\lambda_3=9$ is given by the set of vectors:
$$\begin{bmatrix} 1\\0\\-4 \end{bmatrix}, \begin{bmatrix} -2\\2\\22 \end{bmatrix}$$
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Allister’s father is 120% of Allister’s height. If his father measures 180 cm, then how many centimeters tall is Allister? help plsss
Answer:
Step-by-step explanation:
216
50 points pls help it’s math
The inequalities seen on Cartesian plane are - 2 · x + y > 1 and - (1 / 2) · x + y ≤ 2, respectively.
How to determine the inequalities representing a graph
In this problem we find two graphs by inequalities on Cartesian plane, whose definitions are listed below:
Case 19:
f(x) > y
Case 20:
f(x) ≤ y
Each inequality has a function of the form:
y = m · x + b
Where:
x - Independent variable.y - Dependent variable.m - Slopeb - InterceptAnd the slope can be determined by secant line formula:
m = Δy / Δx
Now we proceed to determine each inequality:
Case 1:
Slope
m = 4 / 2
m = 2
Intercept
b = 1
Inequality
y > 2 · x + 1
- 2 · x + y > 1
Case 2:
Slope
m = 1 / 2
Intercept
b = 2
Inequality
y ≤ (1 / 2) · x + 2
- (1 / 2) · x + y ≤ 2
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Write each expression in terms of sines and/or cosines, and then simplify: 37. sec x / tan x. 38. cot x / csc x 39. sin x / csc x + cos x / sec x 40. 1/sin²x – 1/tan^2 x 41. (1 - sin a)(1 + sin a) 42. (sec a – 1) ( sec a + 1)
43. cos B tan B +1 ) (sin B -1)
44. (1 + cos B) (1 – cot B sin B)
45. 1 + cos a tan a csc a / csc a
46. (cos a tan a + 1 ) ( sin a – 1) / cos^2 a
37. sec x / tan x = (1/cos x) / (sin x/cos x) = cos x / sin x = cot x
38. cot x / csc x = (cos x/sin x) / (1/sin x) = cos x / sin^2 x = cos x * (1/sin^2 x) = cos x * (csc^2 x)
39. sin x / csc x + cos x / sec x = (sin x / 1/sin x) + (cos x / 1/cos x) = sin^2 x + cos^2 x = 1
40. 1/sin²x - 1/tan^2 x = (1/sin^2 x) - (1/(sin^2 x/cos^2 x)) = (1/sin^2 x) - (cos^2 x/sin^2 x) = (1 - cos^2 x)/sin^2 x = sin^2 x/sin^2 x = 1
41. (1 - sin a)(1 + sin a) = 1 - sin^2 a = cos^2 a
42. (sec a - 1)(sec a + 1) = sec^2 a - 1 = tan^2 a
43. (cos B tan B + 1)(sin B - 1) = (cos B * sin B/cos B + 1)(sin B - 1) = (sin B + 1)(sin B - 1) = sin^2 B - 1 = -cos^2 B
44. (1 + cos B)(1 - cot B sin B) = (1 + cos B)(1 - cos B/sin B * sin B) = (1 + cos B)(1 - cos^2 B/sin^2 B) = (1 + cos B)(sin^2 B/sin^2 B - cos^2 B/sin^2 B) = (1 + cos B)(1 - cos^2 B/sin^2 B) = (1 + cos B)(sin^2 B/sin^2 B) = (1 + cos B) * 1 = 1 + cos B
45. 1 + cos a tan a csc a / csc a = 1 + (cos a * sin a/cos a * 1/sin a) / (1/sin a) = 1 + (sin a / sin a) / (1/sin a) = 1 + 1/(1/sin a) = 1 + sin a = sin a + 1
46. (cos a tan a + 1)(sin a - 1) / cos^2 a = (cos a * sin a/cos a + 1)(sin a - 1) / cos^2 a = (sin a + 1)(sin a - 1) / cos^2 a = (sin^2 a - 1) / cos^2 a = -cos^2 a / cos^2 a = -1
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Town A and Town B are located at the points shown in the diagram. Mr. Peterson
wants to drive from Town A to Town B. He can choose between the route that takes
him through Towns P and Q, or the route that takes him through Town R. Each unit on
the grid equals 1 kilometer.
Answer:
To find the shorter route, we need to calculate the distances for both routes and compare them.
Route through Towns P and Q:
The distance between Town A and Town P is 3 units to the right and 5 units up, so it is √(3² + 5²) = √34 km.
The distance between Town P and Town Q is 2 units to the right, so it is 2 km.
The distance between Town Q and Town B is 4 units to the right and 4 units down, so it is √(4² + 4²) = 4√2 km.
Therefore, the total distance for this route is √34 + 2 + 4√2 km.
Route through Town R:
The distance between Town A and Town R is 5 units to the right and 3 units up, so it is √(5² + 3²) = √34 km.
The distance between Town R and Town B is 5 units to the right and 7 units down, so it is √(5² + 7²) = √74 km.
Therefore, the total distance for this route is √34 + √74 km.
Comparing the distances, we can see that:
√34 + 2 + 4√2 km ≈ 10.2 km
√34 + √74 km ≈ 12.6 km
Therefore, the shorter route is the one that goes through Towns P and Q, which is approximately 10.2 km long.
what is 11.5 + 10.5 in math
Answer:
22
Step-by-step explanation:
10+11=21
.05+.05=1
1+21=22
Homework Progress
4/
LEMON SQUASH
2 parts concentrate
to 5 parts water
If you put 90 ml of concentrate in a glass,
how much water should be added?
ml
82%
We need to add 225 ml of water to the 90 ml of concentrate to make lemon squash.
To determine how much water should be added?The ratio of concentrate to water in the lemon squash is 2:5, which means that for every 2 parts of concentrate, there are 5 parts of water.
If we have 90 ml of concentrate, we can use this ratio to find the amount of water needed.
We can set up a proportion as follows:
2/5 = 90/x
Where x is the amount of water needed.
To solve for x, we can cross-multiply:
2x = 5 * 90
2x = 450
x = 225
Therefore, we need to add 225 ml of water to the 90 ml of concentrate to make lemon squash.
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At a restaurant, 600 customers were served during a 10-hour period of time. Which graph has a slope that best represents the number of customers that were served per hour at this restaurant?
Answer: The correct answer would be Graph H.
Step-by-step explanation:
Answer:
top right
Step-by-step explanation:
600 per 10 hours is a rate of 60/hour.
You need a graph that has a slope of 60 and includes the point (1, 60).
Answer: top right
Find a basis of the subspace ofR4defined by the equation−2x1−7x2+2x3−4x4=0. Answer:
A basis for the subspace of R4 defined by the equation−2x1−7x2+2x3−4x4=0 is the set of vectors {(-7/2, 1, 0, 0), (1, 0, 1, 0), (-2, 0, 0, 1)}.
A basis for the subspace of −2x1−7x2+2x3−4x4=0 can be found by solving for one of the variables in terms of the others and then finding the general solution.
First, solve for x1 in terms of the other variables:
-2x1 = 7x2 - 2x3 + 4x4
x1 = (-7/2)x2 + x3 - 2x4
Now, the general solution can be written as:
(x1, x2, x3, x4) = (-7/2)x2 + x3 - 2x4, x2, x3, x4
This can be rewritten in terms of the free variables x2, x3, and x4:
(x1, x2, x3, x4) = x2(-7/2, 1, 0, 0) + x3(1, 0, 1, 0) + x4(-2, 0, 0, 1)
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Solve the system of equation using the method of choice. Show work and steps.
10x+5y=-20
-4x+6y=-8
Answer:
Step-by-step explanation:
1
Dividing Polynon Use synthetic division to divide the polynomi. (3x^(2)+7x+2)+(x+2)
The result of this synthetic division is the quotient (1 2/3 5/3)
To divide two polynomials using synthetic division, we need to write the dividend as a binomial of the form (x-r) and the divisor in its linear form. In this case, the binomial is (x+2) and the linear form is 3x2+7x+2.
Quotient:
3/3=1
2/3=2/3
Coefficients of dividend: 3 7 2
Quotient: 1 2/3
Product of quotient and binomial: (x+2)
(3x2+7x+2) - (x+2): 3x+5 2
Quotient:
3/3=1
2/3=2/3
5/3=5/3
The result of this synthetic division is the quotient (1 2/3 5/3).
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i need helppppppp??????????
Answer:
~7.8
Step-by-step explanation:
side 1 = 5
side 2 = 6
hypotenuse = h
h² = 5² + 6²
h² = 25 + 36
h² = 61
h = [tex]\sqrt{61}[/tex]
h = 7.8102...
Workspace: Given pardlelogram WxY 2, where Wxx =2x+15,xY= x+27 and yz=4x-21, delemine the length of 2W in inches.
The length of 2W in inches can be calculated by using the measurements of the parallelogram. Wxx is 2x+15, and xY is x+27. Since the length of W xx and xY is referring to the same line, x+27=2x+15. Solving for x, x=12. Knowing the value of x, Wxx=2(12)+15=39 inches and xY=12+27=39 inches. Therefore, 2W=2(39)=78 inches.
The length of a line in a parallelogram can be calculated by adding the two measurements of the two lines containing the same point. Since the line containing point W is the same line containing point x, the two measurements can be solved for the same variable, x. Once the variable is determined, the value of the two lines containing the same point can be determined. The value of the two lines can then be multiplied by 2 to determine the length of the line in the parallelogram.
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HELP PLS DUE TDAY
STRESSING
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
how do i answer this
The mass of the solid copper cuboid with dimensions length = 10cm, breadth = 5cm, and height = 3cm, is 1.479 kg.
What is a Cuboid?A cuboid is a three-dimensional geometric shape that has six rectangular faces. It is also known as a rectangular parallelepiped. A cuboid has six rectangular faces, where opposite faces are congruent and parallel. The cuboid has eight vertices, twelve edges, and six rectangular faces.
How to Calculate Mass of a Cuboid?To calculate the mass of a cuboid, you need to know its volume and density. The volume of a cuboid is the product of its length, width, and height. The density of a material is its mass per unit volume. Once you have these values, you can use the following formula to calculate the mass of the cuboid:
Mass = Density x Volume
where Mass is the mass of the cuboid, Density is the density of the material of which the cuboid is made, and Volume is the volume of the cuboid.
In the given question,
Using the given values, we can now calculate the mass of the solid copper cuboid in kg.
The volume of the copper cuboid is:
Volume = Length × Breadth × Height = 10 cm × 5 cm × 3 cm = 150 cm³
The mass of the copper cuboid can be calculated by multiplying its volume with its density. We are given that the density of copper is 9.86 g/cm³. Therefore, we have:
Mass = Volume × Density = 150 cm³ × 9.86 g/cm³ = 1479 g
To convert the mass in grams (g) to kilograms (kg), we need to divide the mass by 1000. Therefore:
Mass in kg = Mass in g / 1000 = 1479 g / 1000 = 1.479 kg
Therefore, the mass of the solid copper cuboid with dimensions length = 10cm, breadth = 5cm, and height = 3cm, is 1.479 kg.
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Assume 12% of a population of credit applications are fraudulent. (i.e each loan has a 12% probability of being fraudulent.)
Based on a random sample of 25 applications find the probability the number of fraudulent applications in the sample is
Equal to 0 [ Select ] Equal to 3 [ Select ] Equal to 3 or less [ Select ] Equal to 5 or more [ Select ] More than 3 [ Select ]
The probability of fraudulent applications are:
Equal to 0 [0.0410] Equal to 3 [0.2387] Equal to 3 or less [0.4088] Equal to 5 or more [0.1734] More than 3 [0.5912]How to determine the probability of fraudulent applicationsThe given parameters are
n = 25
p = 0.12
The individual probability can be calculated as
P(x) = C(n, x) * p^x * (1 - p)^(n - x)
So, we have
Probability the number of fraudulent applications in the sample is 0
P(0) = C(25, 0) * 0.12^0 * (1 - 0.12)^(25 - 0)
P(0) = 0.0410
Probability the number of fraudulent applications in the sample is 3
P(3) = C(25, 3) * 0.12^3 * (1 - 0.12)^(25 - 3)
P(3) = 0.2387
Probability the number of fraudulent applications in the sample is 3 or less
P(x ≤ 3) = P(0) + ... P(3)
Using the formula above, we have
P(x ≤ 3) = 0.4088
Probability the number of fraudulent applications in the sample is 5 or more
P(x ≥ 5) = P(5) + ... P(25)
Using the formula above, we have
P(x ≥ 5) = 0.1734
Probability the number of fraudulent applications in the sample is more than 3
P(x > 3) = 1 - P(x ≤ 3)
By substitution, we have
P(x > 3) = 1 - 0.4088
P(x > 3) = 0.5912
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13. R(x) (2x+6)(x-1) (4-x)(x+2) Find any vertical asymptote(s) and any horizontal asymptote(s)
The vertical asymptote(s) for R(x) is x=1 and x=-2. The horizontal asymptote(s) is y=0.
To find the vertical asymptotes, we look at each factor and look for any x-values that would make the factor equal to zero.
The factors are (2x+6), (x-1), (4-x), and (x+2).
So, x=1 would make (x-1) equal to zero and x=-2 would make (x+2) equal to zero.
To find the horizontal asymptote, we look at the degree of the highest exponent and divide it into the coefficient of the term with the highest degree.
Since the highest exponent is 1 and there is no coefficient, the answer is y=0.
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Suppose you have deposited $1000 into a bank and assume the
account is compounded continuously. If you hope that your balance
will reach to $2000 in 10 years, what is the annual interest rate r
should
The annual interest rate.
To find the annual interest rate r that will allow your balance to reach $2000 in 10 years, we need to use the formula for continuously compounded interest: A = Pert, where A is the final amount, P is the principal amount, r is the annual interest rate, and t is the time in years.
We are given that P = $1000, A = $2000, and t = 10 years. Plugging these values into the formula, we get:
$2000 = $1000e10r
Dividing both sides by $1000, we get:
2 = e10r
Taking the natural logarithm of both sides, we get:
ln(2) = 10r
Dividing both sides by 10, we get:
r = ln(2)/10 ≈ 0.0693
Therefore, the annual interest rate r that will allow your balance to reach $2000 in 10 years is approximately 6.93%.
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A rectangle has the area of 54x8y6
square inches and a length of 9x3y4
. Which expression represents the width of the rectangle?
Responses
The expression that represents the width of the rectangle is 6x^5y^2
Which expression represents the width of the rectangle?We know that the area of a rectangle is given by the formula:
Area = Length x Width
We can rearrange the formula for the area to solve for the width:
Width = Area / Length
From the question, we have the following parameters that can be used in our computation:
Area = 54x^8y^6
Length = 9x^3y^4
Substituting the given values, we get:
Width = (54x^8y^6) / (9x^3y^4)
Evaluate the quotient expression
Width = 6x^5y^2
Hence, the width expression is 6x^5y^2.
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Evaluate the following expressions. Your answer mill be an angle in radians and in the interval [- π/2, π/2]
(a) sin^-1 (1) = ___
(b) sin^-1 (√2 / 2)= ____
(c) sin^-1 (- √2 / 2)= ____
a) The inverse sine of 1 is π/2 radians, which is equivalent to 90 degrees.
b) The inverse sine of √2 / 2 is π/4 radians, which is equivalent to 45 degrees.
c) The inverse sine of - √2 / 2 is -π/4 radians, which is equivalent to -45 degrees.
Evaluate the following expressions. Your answer will be an angle in radians and in the interval [-π/2, π/2]
(a) sin^-1 (1) = π/2
(b) sin^-1 (√2 / 2)= π/4
(c) sin^-1 (- √2 / 2)= -π/4
(a) sin^-1 (1) = π/2
The inverse sine of 1 is π/2 radians, which is equivalent to 90 degrees.
(b) sin^-1 (√2 / 2)= π/4
The inverse sine of √2 / 2 is π/4 radians, which is equivalent to 45 degrees.
(c) sin^-1 (- √2 / 2)= -π/4
The inverse sine of - √2 / 2 is -π/4 radians, which is equivalent to -45 degrees.
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Use the ruler provided to measure the dimensions of the parallelogram shown to the nearest 0.5 centimeter.
Which measurement is closest to the area of the parallelogram in square centimeters?
F.14 cm2
G.16.5 cm2
H. 4114
cm2
J.8.5 cm2
The closest answer choice to 26.25 cm² is G. 16.5 cm².
What is area ?
Area is a measurement of the amount of space inside a two-dimensional figure, such as a square, rectangle, triangle, parallelogram, or circle. It is expressed in square units, such as square centimeters (cm²), square meters (m²), square inches (in²), or square feet (ft²).
Based on the given image, we can use the ruler to measure the dimensions of the parallelogram.
From the ruler, we can see that the base of the parallelogram is approximately 7.5 cm, and the height is approximately 3.5 cm. Therefore, the area of the parallelogram is:
Area = base x height
Area = 7.5 cm x 3.5 cm
Area = 26.25 cm² (rounded to the nearest 0.5 cm)
Among the answer choices provided, the closest one to the calculated area of the parallelogram is 26.5 cm², which is not provided in the answer choices.
Therefore, The closest answer choice to 26.25 cm² is G. 16.5 cm².
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HELP PLS BRAINLIEST AND FIVE STAR IF ALL OF THESE ARE CORRECT
a)√(x^2-14x+49)=x-7
b)√(4x^2-20x+25)=5-2x
C)√(y^4+2y^2+1)=y^2+1
d)√(x^2+2x+1)=x+1
e)√(y^2-20y+100)=y-10
f)√(y^6-2y^3+1)=y^3-1
pls answer all pls pls pls
(also the answer is most likely NOT all real numbers or no solutions)
The solution to the all given equations is that they have infinite many real solutions
How to determine the solution to the equationsEquation (a)
From the question, we have the following parameters that can be used in our computation:
√(x^2-14x+49)=x-7
When both sides of the equations are squared, we have:
x^2 - 14x + 49 = x^2 - 14x + 49
Evaluate the like terms
0 = 0
This represents infinite many solutions
Equation (b)
Here, we have:
√(4x^2-20x+25)=5-2x
When both sides of the equations are squared, we have:
4x^2-20x+25 = 25 - 20x + 4x^2
Evaluate the like terms
0 = 0
This represents infinite many solutions
For the remaining expressions, we have the following (using the above steps)
Equation (c)
√(y^4+2y^2+1) = y^2 + 1
y^4 + 2y^2 + 1 = y^4 + 2y^2 + 1
0 = 0
Equation (d)
√(x^2+2x+1)=x+1
x^2 + 2x + 1 = x^2 + 2x + 1
0 = 0
Equation (e)
√(y^2-20y+100)=y-10
y^2 - 20y + 100 = y^2 - 20y + 100
0 = 0
Equation (f)
√(y^6-2y^3+1)=y^3-1
y^6-2y^3+1 = y^6-2y^3+1
0 = 0
Hence, the equations have infinite solutions
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James created a scale drawing of the school library in his art class. In the scale drawing, the length of the library is 13 inches. The length of the actual library is 78 feet. Which scale did James use to create the scale drawing of the school library?
The scale unit that James used to create scale drawing of school library is 1 inch = 6 feet.
What is scale unit?A measurement scale used to represent actual dimensions in a model or drawing. Scales include units of measurement such as inches, feet, and meters, scale unit. A scale used to represent actual dimensions on a drawing or map.
What is scale drawing?A scale map is a two-dimensional representation of a real-world object or place. Maps and floor plans are examples of scale drawings. The scale shows what the length on the scale drawing represents in actual length .
According to the question:
Given, 78 feet length of library is represented by 13 inch
Let, "x" be the number of feet that 1 inch represents.
∴ 13x = 78 feet
⇒x = 78/13
⇒x = 6
So, 1 inch equals 6 feet.
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Answer:
the answer would be 1 inch = 6 feet
Step-by-step explanation:
What is scale unit?
A measurement scale used to represent actual dimensions in a model or drawing. Scales include units of measurement such as inches, feet, and meters, scale unit. A scale used to represent actual dimensions on a drawing or map.
What is scale drawing?
A scale map is a two-dimensional representation of a real-world object or place. Maps and floor plans are examples of scale drawings. The scale shows what the length on the scale drawing represents in actual length .
Solution:
Given, 78 feet length of library is represented by 13 inch
Let, "x" be the number of feet that 1 inch represents.
∴ 13x = 78 feet
⇒x = 78/13
⇒x = 6
So, 1 inch equals 6 feet.
