Ebba is buying bulk fabric.
She is shopping for the best deal.

Drag the fabric in order from the least to the greatest unit cost in dollars per square yard.

The value of the absolute percent error for week 3 is 25.00%.

To calculate the absolute percent error for week 3, we need to find the absolute difference between the forecasted value and the actual value, and then divide it by the actual value. Finally, we multiply the result by 100 to convert it to a percentage.

To find the absolute percent error for week 3, we'll use the formula:

Absolute Percent Error = |(Actual Value - Forecasted Value) / Actual Value| * 100

For week 3:

Actual Value = 4.00

Forecasted Value = 3.00

Absolute Percent Error = |(4.00 - 3.00) / 4.00| * 100

= |1.00 / 4.00| * 100

= 0.25 * 100

= 25.00

Therefore,For week three, the absolute percent error value is 25.00%.

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Answer:

60 mph

Step-by-step explanation:

We calculate the combined distance travelled by the two trains in two hours.

As they were 500 miles apart at first, and 300 miles apart after, they have travelled 200 miles together.

I think the question means "one train travels 20 mph faster than the other".

Say the faster train has speed x mph. Then the slower has speed x - 20 mph.

Now, the combined distance travelled in 2 hrs is 2 * (x + x - 20) = 200

2x - 20 = 100

2x = 120

x = 60 mph

Answer: h(x) = 23

Step-by-step explanation:

Plug x in the equation

h(x) = 4(7) - 5

h(x) = 28 - 5

h(x) = 23

Answer:

He can select a row of the random number table and read 20 single digits between 1 and 5. He will record the number of digits that are a 1.

Step-by-step explanation:

edge 2022

Option matching to all our reasoning is:

He can select a row of the random number table and read 20 single digits between 1 and 5. He will record the number of digits that are a 1.

The sampling distribution is the process of collecting data from a very large population.

In the question, we are informed that the dean of students is doing a sampling distribution of students, to find out the number of students enrolled in a nursing program. The table is assigned by digits, where the outcomes of the digits are as follows:

1 = student enrolled in nursing program

2–5 = Students not enrolled in nursing program

Skip 6–9 and 0.

We need to simulate one trial of the situation, where the dean of students selects a random sample of 20 students and records n = the number of students enrolled in the nursing program.

To simulate this, we need a sample from the table with 20 values, so the dean will read 20 single digits between 1 and 5, as these digits are only assigned data, the rest have been asked to skip. To calculate n = the number of students enrolled in the nursing program, we will record the number of digits that are a 1, because 1 represents a student enrolled in the nursing program.

Option matching to all our reasoning is:

He can select a row of the random number table and read 20 single digits between 1 and 5. He will record the number of digits that are a 1.

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well, we know the angles at E and D are both 130°, and the other four angles are all equal hmmm let's call them hmmm "x".

\(\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ S = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ n=6 \end{cases}\implies S=180(6-2)\implies S=720 \\\\[-0.35em] ~\dotfill\\\\ x+x+x+x+130+130~~ = ~~720\implies 4x+260=720 \\\\\\ 4x=460\implies x=\cfrac{460}{4}\implies x=115^o~~ = ~~\measuredangle BAF\)

The size of angle BAF in the hexagon ABCDEF is 92°. This is determined by applying the properties of regular hexagons and solving for the value of x, which represents angle BAF.

To find the size of angle BAF in the hexagon ABCDEF, we'll use the information given and apply the properties of regular hexagons and the angles of triangles.

Given information:

Angle BAF = Angle ABC = Angle AFE = Angle BCD (let's call this angle x).

Angle DEF = Angle CDE = 130°.

Since the sum of the interior angles of a hexagon is (6-2) × 180° = 720°, we can write the equation:

x + x + 130° + x + x + 130° = 720°

Simplify the equation:

5x + 260° = 720°

Now, solve for x:

5x = 720° - 260°

5x = 460°

x = 460° / 5

x = 92°

Now that we have the value of angle x, which is 92°, we can find angle BAF:

Angle BAF = x = 92°

So, the size of angle BAF is 92°.

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Answer:

96 square tiles are needed

Step-by-step explanation:

To calculate this, the first thing we need to do is calculate the total area covered by the rectangular wall.

Mathematically, the area of the rectangle = 16 * 24 = 384 ft^2

The next thing we need to do is calculate the area of the square tiles = L^2 = 2^2 = 4 ft^2

the number of square tiles needed = Area of rectangular wall/Area of square tiles = 384/4 = 96

Answer:

To convert base A log to base B log, use the formula:

logAx = (logBx)/(logBA)

So, to convert log134 to natural logs (base e).

      log134 = (loge4)/(loge13) = ln4/ln13

Step-by-step explanation:

When a polynomial p(x) is divided by a linear polynomial (x - a), then the remainder is equal to p(a).

To find the remainder we need:

As result we get the remainder.

             x - 5 = 0    ⇔   x = 5

Substitute 5 to x³ + 8x² + 11x - 20:

5³ + 8×5² + 11×5 - 20 = 125 + 8×25 + 55 - 20 = 160 + 200 = 360

So:

The equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 is proven by mathematical induction.

We have,

To prove the equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 using mathematical induction,

We will follow the three steps of mathematical induction:

The base case, the induction hypothesis, and the inductive step.

Step 1: Base case

Let's start by checking if the equation holds true for the base case, which is n = 1.

When n = 1, the left-hand side (LHS) is 1² = 1, and the right-hand side (RHS) is 1(1 + 1)(2(1) + 1) / 6 = 1.

Since LHS = RHS for the base case, the equation holds true.

Step 2: Induction hypothesis

Assume the equation holds true for some positive integer k, where k ≥ 1. This is our induction hypothesis:

1 + 4 + 9 + ... + k² = k(k + 1)(2k + 1) / 6

Step 3: Inductive step

We need to prove that if the equation holds true for k, it also holds true for k + 1.

Starting with the left-hand side of the equation, we add (k + 1)² to both sides:

1 + 4 + 9 + ... + k² + (k + 1)² = k(k + 1)(2k + 1) / 6 + (k + 1)²

Simplifying the right-hand side:

= [k(k + 1)(2k + 1) + 6(k + 1)²] / 6

= [(2k³ + 3k² + k) + (6k² + 12k + 6)] / 6

= (2k³ + 9k² + 13k + 6) / 6

= [(k + 1)(k + 2)(2k + 3)] / 6

We can see that the right-hand side is now in the form

(k + 1)((k + 1) + 1)(2(k + 1) + 1) / 6, which matches the equation for k + 1.

Since the equation holds true for k implies it holds true for k + 1, and the base case is true, we have proven the equation using mathematical induction.

Therefore,

The equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 is proven by mathematical induction.

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Answer:

g(x) = 3·sin(x + π/2) - 4

Step-by-step explanation:

The given (general form of a) sin function is g(x) = A·sin(x + C) + D

Where;

A = The amplitude (the vertical stretch) = 3

C = The phase shift, left = π/2

D = The vertical shift = 4 units down = -4

Therefore, given that in the parent function, we have f(x) = sin(x), by substituting the values of A, C, and D to complete the equation modeling the function g, we get;

g(x) = 3·sin(x + π/2) - 4

The 4 tests for similar triangles are:-

AAA: Three pairs of equal angles.

SSS: Three pairs of sides in the same ratio.

SAS: Two pairs of sides in the same ratio and an equal included angle.

ASA: Two angles and the side included between the angles of one triangle are equal

What is AAA,SAS,ASA,SSS?

According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle. 

According to the SAS rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle.

According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle.

According to the  AAA rule, "if in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion), and hence the two triangles are identical."

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The adjoint of the matrix A is adj(A) = [-4 5 0 -5 4 1 -7 3 -1]. The inverse of A exists A^-1 = [4/32 -5/32 0 5/32 -4/32 -1/32 7/32 -3/32 1/32].

To find the adjoint of a matrix A, we need to find the transpose of its cofactor matrix. The cofactor matrix of A is obtained by taking the determinants of the 2x2 matrices formed by crossing out each element of A and then multiplying them by -1 or 1 in a checkerboard pattern.

Using this method, we get:

Cof(A) = [7 -3 1 -4 -7 1 5 4 -5]

Taking the transpose of Cof(A), we get the adjoint of A:

adj(A) = [-4 5 0 -5 4 1 -7 3 -1]

To find the inverse of A, we use the formula:

A^-1 = adj(A) / det(A)

where det(A) is the determinant of A.

The determinant of A can be found by expanding along the first row:

det(A) = -4(4(-1) - 3(1)) - 5(5(-1) - 3(0)) + 7(5(1) - 4(0))

= -4(-4) - 5(-5) + 7(5)

= 16 + 25 + 35

= 76

Therefore, we have:

A^-1 = adj(A) / det(A) = [-4 5 0 -5 4 1 -7 3 -1] / 76

A^-1 = [4/32 -5/32 0 5/32 -4/32 -1/32 7/32 -3/32 1/32]

So, the inverse of A exists and is given by the above matrix.

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Answer:

A. 232 acres

Step-by-step explanation:

Got it right

The number of acres of land that were harvested is given by A = 232 acres

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the total amount of harvest of bushels be = 9,396 bushels

And , the amount of bushels per acre = 40.5

So , number of acres of land that were harvested is A = amount of harvest of bushels / amount of bushels per acre

On simplifying the equation , we get

The number of acres of land that were harvested is A = 9,396 / 40.5

The number of acres of land that were harvested is A = 232 acres

Hence , the number of acres is 232 acres

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Step-by-step explanation:

The root is

-sqr root of 5.

First, we put these roots in the forn of

\((x - a)\)

where a is the root

So we have

\((x - ( - 2))(x - \sqrt{5} )(x - \frac{10}{3} )\)

\((x + 2)(x - \sqrt{5} )(3x - 10)\)

\((3 {x}^{2} - 4x - 20)(x - \sqrt{5} )\)

To get rid of that square root, let have another root that js the conjugate posive root of 5.

\((3 {x}^{2} - 4x - 20)(x - \sqrt{5} )(x + \sqrt{5} )\)

\((3 {x}^{2} - 4x - 20)(x {}^{2} + 5)\)

Which will gives us a rational coeffeicent of degree 4.

Why we didn't do

\((x - \sqrt{5} )\)

?

Because

\((x - \sqrt{5} ) {}^{2} = {x}^{2} - 2 \sqrt{5} + 5\)

If we foiled out we will still have a irrational coeffceint.

Answer:

:

Example Question #1:

Step-by-step explanation:

Which of the following is the equation of a line that is parallel to the line 4x – y = 22 and passes through the origin?

Possible Answers:

4x – y = 0

(1/4)x + y = 0

4x + 8y = 0

4x = 8y

y – 4x = 22

Correct answer:

4x – y = 0

Explanation:

We start by rearranging the equation into the form y = mx + b (where m is the slope and b is the y intercept); y = 4x – 22

Now we know the slope is 4 and so the equation we are looking for must have the m = 4 because the lines are parallel. We are also told that the equation must pass through the origin; this means that b = 0.

In 4x – y = 0 we can rearrange to get y = 4x. This fulfills both requirements.

', .

Answer:

7. the slope of the line containing the points (3, 4) and (2, 6) is -2.

8. the slope of the line containing the points (-2, -1) and (2, -3) is -1/2.

Step-by-step explanation:

7. To find the slope of a line that is parallel to the line containing the points (3, 4) and (2, 6), we first need to find the slope of the line through those two points using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (3, 4) and (x2, y2) = (2, 6). Substituting these values into the formula, we get:

m = (6 - 4) / (2 - 3) = -2

So the slope of the line containing the points (3, 4) and (2, 6) is -2. Since we are looking for a line that is parallel to this line, the slope of the parallel line will also be -2. Therefore, the answer is m = -2.

8. To find the slope of a line that is perpendicular to the line containing the points (-2, -1) and (2, -3), we first need to find the slope of the line through those two points using the same formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) = (-2, -1) and (x2, y2) = (2, -3). Substituting these values into the formula, we get:

m = (-3 - (-1)) / (2 - (-2)) = -2 / 4 = -1/2

So the slope of the line containing the points (-2, -1) and (2, -3) is -1/2. To find the slope of a line that is perpendicular to this line, we need to take the negative reciprocal of -1/2, which is 2/1 or simply 2. Therefore, the answer is m = 2.

1.5x-0.5 should be the answer

In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.

The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.

We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.

Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.

Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000

We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)

Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0

Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.

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Answer:

Step-by-step explanation:

We can conclude that if H and K are subgroups of G, then H ∩ K is also a subgroup of G.

Let H and K be two subgroups of G. Then we can prove that H ∩ K is also a subgroup of G.Proof:

We have to prove that H ∩ K is closed under multiplication, contains the identity element, and contains the inverse of each of its elements.. Closure under multiplicationLet a, b be two elements of H ∩ K.

Then, a, b belong to both H and K. Since H and K are both subgroups of G, a * b also belongs to both H and K. Therefore, a * b ∈ H ∩ K.

Thus, H ∩ K is closed under multiplication. Identity elementLet e be the identity element of G. Since H and K are subgroups of G, e ∈ H and e ∈ K.

Therefore, e ∈ H ∩ K. Thus, H ∩ K contains the identity element.3. Inverse elementLet a be an element of H ∩ K. Then a ∈ H and a ∈ K.

Since H and K are subgroups of G, a⁻¹ ∈ H and a⁻¹ ∈ K. Therefore, a⁻¹ ∈ H ∩ K. Thus, H ∩ K contains the inverse of each of its elements.

Therefore, we can conclude that H ∩ K is a subgroup of G. Answer more than 100 words:When we are dealing with groups, the intersection of two subgroups is itself a subgroup.
This is because, to be a group, we only need to satisfy the four axioms of a group.

The closure under multiplication is satisfied because if two elements belong to each subgroup, then they belong to the intersection of the subgroups.

The identity and inverse are also preserved because the identity and inverse of an element are always contained in the subgroups. Finally, associativity is always satisfied.

Thus, we can conclude that if H and K are subgroups of G, then H ∩ K is also a subgroup of G.

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A major disadvantage of electron microscopes compared to light microscopes is that they cannot be used to view live specimens. Therefore, option B is the correct answer.

A major disadvantage of electron microscopes compared to light microscopes is that they cannot be used to view live specimens. This is because the electron microscope requires a vacuum environment to function properly, which would kill any live specimen. Additionally, electron microscopes can only see surface details and do not have a very high power of resolution. Lastly, electron microscopes can only be used by doctors or trained technicians, so they are not as widely available as light microscopes.

Therefore, option B is the correct answer.

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A disadvantage of electron microscopes compared to light microscopes is that they cannot be used to view live specimens (option b). Electron microscopes use a beam of electrons to create an image, which requires a vacuum environment. This means that living organisms cannot survive in the vacuum and therefore cannot be observed with electron microscopes.

I hope this helped! :)

The solution to the given initial value problem, obtained using Laplace transforms, is y(x) = 0. This means that the function y(x) is identically zero for all values of x.

To find the solution of the initial value problem using Laplace transforms for the equation d²y/dx² + 9y = 9sin(t)u(t - 3), where y(0) = y'(0) = 0, we can follow these steps:

Take the Laplace transform of the given differential equation.

Applying the Laplace transform to the equation d²y/dx² + 9y = 9sin(t)u(t - 3), we get:

s²Y(s) - sy(0) - y'(0) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Since y(0) = 0 and y'(0) = 0, the Laplace transform simplifies to:

s²Y(s) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Solve for Y(s).

Combining like terms, we have:

Y(s) * (s² + 9) = 9 * (1/s² + 1/(s² + 1))

Multiply through by (s² + 1)(s² + 9) to get rid of the denominators:

Y(s) * (s⁴ + 10s² + 9) = 9 * (s² + 1)

Simplifying further, we have:

Y(s) * (s⁴ + 10s² + 9) = 9s² + 9

Divide both sides by (s⁴ + 10s² + 9) to solve for Y(s):

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9)

Partial fraction decomposition.

To proceed, we need to decompose the right side of the equation using partial fraction decomposition:

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9) = A/(s² + 1) + B/(s² + 9)

Multiplying through by (s⁴ + 10s² + 9), we have:

9s² + 9 = A(s² + 9) + B(s² + 1)

Equating the coefficients of like powers of s, we get:

9 = 9A + B

0 = A + B

Solving these equations, we find:

A = 0

B = 0

Therefore, the decomposition becomes:

Y(s) = 0/(s² + 1) + 0/(s² + 9)

Inverse Laplace transform.

Taking the inverse Laplace transform of the decomposed terms, we find:

L^(-1){Y(s)} = L^(-1){0/(s² + 1)} + L^(-1){0/(s² + 9)}

The inverse Laplace transform of 0/(s² + 1) is 0.

The inverse Laplace transform of 0/(s² + 9) is 0.

Combining these terms, we have:

Y(x) = 0 + 0

Therefore, the solution to the initial value problem is:

y(x) = 0

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The procedure for revising probabilities based on additional information is referred to as Bayesian updating

The procedure for revising probabilities based on additional information is referred to as Bayesian updating. Bayesian updating is a fundamental concept in Bayesian statistics, which allows for the incorporation of new evidence or data to update and refine prior beliefs or probabilities.

In Bayesian updating, the process begins with an initial prior probability, which represents the initial belief or knowledge about an event or hypothesis before any evidence is observed. As new evidence or data becomes available, it is used to update the prior probability and generate a posterior probability. The posterior probability represents the revised belief or probability after incorporating the new information.

Bayesian updating follows the principles of Bayes' theorem, which mathematically describes the relationship between prior probabilities, likelihoods, and posterior probabilities. It involves combining the prior probability with the likelihood of observing the data given the hypothesis and then normalizing the result to obtain the posterior probability.

The beauty of Bayesian updating is that it allows for a flexible and iterative process of continuously updating beliefs and probabilities as new information emerges. It provides a framework for incorporating both subjective prior beliefs and objective data to make more informed decisions and predictions. Bayesian updating has applications in various fields, including machine learning, decision-making, and scientific research.

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True. The multiplicity of a root r of the characteristic equation of matrix A is indeed called the algebraic multiplicity of r as an eigenvalue of A.

The characteristic equation of a square matrix A is obtained by subtracting λI (where λ is an eigenvalue and I is the identity matrix) from A and taking its determinant. The roots of this equation are the eigenvalues of matrix A.

The algebraic multiplicity of an eigenvalue r refers to the number of times r appears as a root of the characteristic equation. In other words, it represents the multiplicity of r as a solution of the equation.

The algebraic multiplicity provides information about the behavior of the eigenvalue r within the matrix A. If the algebraic multiplicity of r is greater than 1, it means that r is a repeated eigenvalue and there exist multiple linearly independent eigenvectors associated with it. On the other hand, if the algebraic multiplicity is 1, r is a simple eigenvalue, indicating that there is only one linearly independent eigenvector corresponding to r.

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In statistics, a scatter plot is used to identify a correlation between two variables by visually observing a collection of ordered pairs (x, y) in which two variables are plotted on the X and Y axis. The value of one variable is compared to the value of the other variable. The data can be measured and presented on a graph to determine whether there is a relationship between them. A scatter plot of home run leaders for each league in baseball is one such example.

To construct a scatter plot of home run leaders in baseball, the difference between the smallest and largest number of home runs by leaders for each league must first be calculated. The American League and the National League are the two leagues in baseball that have home run leaders. A scatter plot of home run leaders can be constructed using a graph. The vertical axis represents the number of home runs hit by the leaders in the National League.

The horizontal axis represents the number of home runs hit by the leaders in the American League. The difference between the greatest and smallest number of home runs hit by the leaders in each league will be measured. To get the difference between the smallest and greatest number of home runs in each league, the greatest number of home runs hit by leaders in a league is subtracted from the smallest number of home runs hit by leaders in a league.

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Answer:

option 'C' is the correct one or parent function of linear.

Steps of Construction:

1. Draw a line segment BC = 6 cm.

2. Draw a perpendicular bisector of BC that intersects the line BC at Q.

3. Mark A on the line such that OA = 4 cm.

4. Join A to B and C.

5. Draw a ray BX making an acute angle with BC.

6. Mark four points B1,B2, B3, and B4 on the ray BX. such that BB1 = B1B2 = B2B3 = B3B4.

7. Join B4C. Draw a line parallel to B4C through B3 intersecting line segment AB at A'.

Hence ΔA'BC' is the required triangle.

An isosceles triangle is a type of triangle that has two equal sides and two equal angles. The third angle is called the base angle and is typically different from the other two angles. The equal sides are called legs, and the third side is called the base.

Isosceles triangles have some interesting properties. One of them is that the base angles are always equal. This means that if you know the measure of one of the base angles, you can find the measure of the other one by subtracting it from 180 degrees and dividing by 2. Another property is that the altitude from the apex (the point opposite the base) always bisects the base, meaning that it cuts the base into two equal parts.

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Complete Question:

Construct an isosceles triangle whose base is 6 cm and altitude 4 cm. Then construct another triangle with sides are 3/4 the corresponding sides  of the isosceles triangle.

Answer:

hypotenuse=h

h = 1 + 1,5

h= 2,5

h²= catheto²+catheto²

2,5² = 1,5² + x²

x²= 2,5² - 1,5²

x²= 6,25 - 2,25

x²=4

now you have to do the square root of 4 which is 2 (2×2 = 4)

x= 2