Final answer:
The correct approach to constructing a parallelogram is to measure equal segments on parallel lines and then join the endpoints of these segments, which ensures opposite sides are equal and parallel.
Explanation:
The student has asked which of the following approaches can be used to construct a parallelogram. The correct approach is Measure equal segments on parallel lines, then join the endpoints of these segments, which corresponds to option a. This method utilizes the properties of parallelograms, where opposite sides are equal in length and parallel to each other. The Euclidean Geometry postulates that relate to this method include E1 Two points determine a line, E2 Line segments can be extended, and the Parallel postulate: Given a line and a point not on the line, no more than one line can be drawn through the point and parallel to the given line.
To construct a parallelogram, you can follow these simplified steps:
Select any two parallel lines.
Measure and mark equal length segments on each of the lines.
Join the corresponding endpoints of these segments to form the parallelogram.
which shows the factored form of x2-12x-45
Answer:
[tex](x+3)(x-15)[/tex] is the required factorized form of the given expression.
Step-by-step explanation:
The given equation is:
[tex]x^2-12x-45[/tex], we have to factorized this equation,
Upon solving the above equation, we get
⇒[tex]x^2-15x+3x-45[/tex]
⇒[tex]x(x-15)+3(x-15)[/tex]
⇒[tex](x+3)(x-15)[/tex]
which is the required factorized form of the given expression.
The longest side of an acute isosceles triangle is 8 centimeters. Rounded to the nearest tenth, what is the smallest possible length of one of the two congruent sides? 4.0 cm 4.1 cm 5.6 cm 5.7 cm
The smallest possible length of one of the two congruent sides is 5.7 cm and this can be determined by using the Pythagorean theorem for an acute triangle.
Given :
The longest side of an acute isosceles triangle is 8 centimeters.
The following steps can be used in order to determine the smallest possible length of one of the two congruent sides:
Step 1 - The Pythagorean theorem for an acute triangle can be used in order to determine the smallest possible length of one of the two congruent sides.
Step 2 - Let the length of the smaller sides be 'a' and let the length of the larger side be 'b'.
Step 3 - According to the Pythagorean theorem for an acute triangle:
[tex]\rm H^2 < B^2+P^2[/tex]
where H is the hypotenuse, B is the base, and P is the perpendicular.
Step 4 - Substitute the values of the known terms in the above expression.
[tex]a^2+a^2>b^2[/tex]
[tex]2a^2>b^2[/tex]
Step 5 - Substitute the value of x in the above expression.
[tex]2a^2>8^2[/tex]
a > [tex]\sqrt{32}[/tex]
a > 5.6
Therefore, the correct option is D).
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What is the degree measure of the supplement of the complement of a 42-degree angle?
Grace was given the description “three less than the quotient of a number squared and nine, increased by eight” and was asked to evaluate it when n = 6. Her work is shown below.
Step 1: mc021-1.jpg
Step 2: mc021-2.jpg
Step 3: mc021-3.jpg
Step 4: mc021-4.jpg
Step 5: 7
In which step did she make an error?
step 1
step 2
step 4
step 5
Grace made an error in Step 5 of evaluating the expression 'three less than the quotient of a number squared and nine, increased by eight' when n = 6. The correct evaluation should result in 12, not 7 as she calculated. Hence, the error is in Step 5, where she incorrectly concluded that the expression equals 7.
Explanation:The question asks us to identify the step at which Grace made an error in evaluating the expression given the description “three less than the quotient of a number squared and nine, increased by eight” when n = 6. Without seeing the exact steps Grace took, we can still solve the expression ourselves.
Firstly, let's translate the description into an algebraic expression using n as our number:
“Three less than the quotient of a number squared and nine” can be expressed as ((n^2)/9) - 3.
Then, we “increase by eight” to get the final expression: ((n^2)/9) - 3 + 8.
If n = 6, we substitute in the value to get: ((6^2)/9) - 3 + 8, which simplifies to (36/9) - 3 + 8 = 4 + 8 = 12.
Thus, the correct answer when evaluating the expression for n = 6 is 12. Grace's error appears to have occurred in Step 5, where she incorrectly evaluated the final sum as 7.
What is the coefficient of y in the expression 3 ⋅ 4 + 5y?
5
9
12
17
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NEED URGENT HELP!
The table shows the height of a plant as it grows.
a. Model the data with an equation.
b. Based on your model, predict the height of the plant at 12 months
Which of these shows 7 + 2y rewritten using the commutative property of addition?
7y + 2
2y + 7
7 − 2y
2y − 7
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Barbara sells iced tea for $1.49 per bottle and water for $1.25 per bottle. She wrote an equiation to find the number of drinks she needs to sell to sell to earn $100
Triangle xyz is reflected across the y axis and x = 4,-5 what are the coordinates of x
Answer:
[tex]\tilde{x}=(-4,-5)[/tex]
Step-by-step explanation:
When we reflect a point [tex]P=(p_x,p_y)[/tex] over the y-axis, it's reflected to the point [tex]\tilde{P}[/tex] with the same y-coordinate as P and whose x-coordinate is minus the x-coordinate of P, hence
[tex]\tilde{P}=(-p_x,p_y).[/tex]
Therefore, in our particular case the point x=(4,-5) is reflected to the point
[tex]\tilde{x}=(-4,-5).[/tex]
would you ever get a credit card from a company that would raise your rate even though you pay your credit card bills as agreed?
a.i don't mind throwing money away
b.i didn't now that credit card companies from one another
c.i didn't carefully shop for the right credit card company.
d.both b and c
A box of grass seed weighs .62 pounds. How much does a box containing .75 times as much grass seed weigh?
You are stacking books into a shipping box that is 15 inches high. Each book is 1.25 inches thick. How many books can you fit in a stack?
NEED HELP FAST!!
Which statement is true about the equation 3/4 z = 1/4 z - 3 + 5?
It has no solution.
It has one solution
It has two solutions.
It has infinitely many solutions.
Translate the sentence into an inequality.
Six subtracted from b is at most 21.
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How to solve 19-4c=17?
Which function is an example of exponential growth? y = 2(0.3)x y = 1.5(0.4)x y = 3(8)x y = 2(0.7)x
In the equation y = 3x - 1 what is the value of y when x equals -3?
Just plug in -3 for x and solve
y= -10
Is 5 3/7 real and irrational or real and rational?
given f(x)=6x+2 find f(x+3)
f(x+3) = 6x+20
What is a function?A function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
f(x) = 6x+2
f(x+3) = 6(x+3) + 2
= 6x + 18 + 2
= 6x + 20
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On Ms. Smith's last math test, 60% of her 25 students earned an 83% or better. How many of Ms. Smith's students earned an 83% or better on the last math test? A. 17 B. 14 C. 20 D. 15
The answer is 15.
15 students earned an 83% or better on the last math test.
60% of 25 students means 60% * 25 = 15 students earned an 83% or better on Ms. Smith's last math test. Therefore, the answer is 15.
P = KT/V solve for k
we have
[tex]P=\frac{KT}{V}[/tex]
Solve for K means clear the variable K
so
Multiply both sides by [tex]V[/tex]
[tex]PV=V\frac{KT}{V}[/tex]
[tex]PV=KT[/tex]
Divide both sides by [tex]T[/tex]
[tex]PV/T=KT/T[/tex]
[tex]K=PV/T[/tex]
therefore
the answer is
[tex]K=PV/T[/tex]
Solve the following system. 4x2 + 9y2 =72 x2 - y2 = 5 The solutions are (), (), (), and () (remember to include the commas) there has to be 4 solutions all ordered pairs please help
Answer: The required solutions are
[tex](x,y)=(3,2),~(-3,2),~(3,-2),~(-3, -2).[/tex]
Step-by-step explanation: We are given to solve the following system of equations:
[tex]4x^2+9y^2=72~~~~~~~~~~~~~~~~~~~~(i)\\\\x^2-y^2=5~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Let us consider that
[tex]x^2=a,~~~~~y^2=b.[/tex]
So, equations (i) and (ii) becomes
[tex]4a+9b=72~~~~~~~~~~~~~~~~(iii)\\\\a-b=5~~~~~~~~~~~~~~~~~~~~(iv)[/tex]
Multiplying equation (iv) by 4 and then subtracting from equation (iii), we get
[tex](4a+9b)-(4a-4b)=72-4\times 5\\\\\Rightarrow 4a+9b-4a+4b=72-20\\\\\Rightarrow 13b=52\\\\\Rightarrow b=4.[/tex]
From equation (iv), we get
[tex]a-b=5\\\\\Rightarrow a-4=5\\\\\Rightarrow a=9.[/tex]
Therefore,
[tex]a=9~~~~~\Rightarrow x^2=9~~~~~\Rightarrow x=\pm3,\\\\b=4~~~~~\Rightarrow y^2=4~~~~~\Rightarrow y=\pm2.[/tex]
Thus, the required solutions are
[tex](x,y)=(3,2),~(-3,2),~(3, -2),~(-3, -2).[/tex]
True or False: Every Student's t-distribution with n < N, n the number in the sample and N the number in the population, will be less peaked and have thinner tails.
The statement is false as the Student's t-distribution is actually more peaked and has thicker tails with smaller sample sizes, and it becomes similar to the standard normal distribution as the sample size, and consequently the degrees of freedom, increase.
Explanation:The statement that every Student's t-distribution with n < N, where n is the sample size and N is the population size, will be less peaked and have thinner tails is false. In reality, the t-distribution is more peaked and has thicker tails when the sample size is smaller, which happens due to the reduced degrees of freedom (df).
The shape of the Student's t-distribution is determined by the degrees of freedom, which is n - 1 for a sample size n. As n approaches the population size N, the t-distribution approaches the standard normal distribution. This is further supported by the central limit theorem, which states that as the sample size increases, the sampling distribution of the sample means tends to be normal. Therefore:
The statement in the question is false; the t-distribution becomes less peaked and has thicker tails as the degrees of freedom decrease.
Explanation:The Student's t-distribution is a probability distribution that is used when the sample size is small and the population standard deviation is unknown. It is similar to the standard normal distribution, but has thicker tails and less probability in the center. As the degrees of freedom increase, the t-distribution approaches the standard normal distribution. Therefore, the statement in the question is false. The t-distribution becomes less peaked and has thicker tails as the degrees of freedom decrease.
At a physics convention, 10 companies set up equal sized square booths in a row along one wall of the convention center. The booths are adjacent to each other and a 4-ft wide walkway surrounds the block of booths on three sides. The total area of the booths and walkway is 2300 ft2. What is the side length of each booth?
A scale on a map says that 1 inch represents 60 miles. If the distance between two points on the map is 2 1/2 inches, how many miles are between the two points?
To find the number of miles between the two points, we need to calculate the distance represented by 2 1/2 inches on the map.
Given that the scale states 1 inch represents 60 miles, we can use this information to determine the distance in miles represented by each inch on the map. So, if 1 inch equals 60 miles, then we can write this as the ratio: 1 inch / 60 miles. To find the distance represented by 2 1/2 inches on the map, we can multiply the ratio by the number of inches: [tex](2 1/2 inches) × (1 inch / 60 miles)[/tex]. Simplifying this expression, we get: ([tex]5/2 inches) × (1 inch / 60 miles).[/tex]
Now, we can multiply the numerators and denominators together: [tex](5/2) × (1/60) = 5/120 = 1/24[/tex]. Therefore, [tex]2 1/2 i[/tex]nches on the map represents 1/24 of the actual distance between the two points. Now, to find the actual distance in miles, we can divide 60 miles (representing 1 inch on the map) by 24: 60 miles [tex]/ 24 = 2.5[/tex] miles. Thus, the two points on the map are approximately 2.5 miles apart from each other in actual distance.
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3/8 of the people at a fun fair were children 3/4 of the remaining people were men there were 140 children than women how many people went to the funfair
Tony misplaced 7 stamps from his collection. He knows that each stamp of his worth $0.15 and that the total value of them is now only $5.55. write an -EQUATION- to determine the number of stamps (s) that tony originally had.
Which of this is tru
I need help with #46!!!!
Remark
There are two formulas for doing this. I'll use the one that does not involve the slope. I think it will be easier for you to understand.
Step One
Decide which point is (x1,y1)
Since point P is 2/5 the way up from point A, we will call (x1,y1) point A
Step Two
Write the givens.
Point(A) = (-2,-3)
Point(B) = (3,2)
Step Three
Write the formula
x1 + ratio*(x2 - x1), y1 + ratio(y2 - y1)
Sub and solve.
-2 + 2/5 *(3 - - 2) , -3 + 2/5*(2 - -3)
-2 + 2/5(5) , - 3 + 2
-2 + 2 , - 1
P = (0 , - 1) <<<<<< Answer
If this turns out to be incorrect please notify me.