Please help with proof, if correct will give points

An equation highlighting the discount: y = (65 - 7)x

A simpler equation: y = 58x

If one angle in an isosceles triangle is 90 degrees then the measure of each angle of an isosceles triangle will be 45 degrees

What is an isosceles triangle ?

A triangle with two equal sides is said to be isosceles. Also equal are the two angles that face the two equal sides. In other terms, an isosceles triangle is a triangle with two sides that have the same length.

If the sides AB and AC of a triangle ABC are equal, then the triangle ABC is an isosceles triangle with B = C. "If the two sides of a triangle are congruent, then the angle opposite to them is likewise congruent," states the theorem that characterizes the isosceles triangle.

Since this triangle's two sides are equal, the base of the triangle is the side that is not equal.

As we know that in an isosceles triangle set of two angles are equal

And

we also know that sum of all the angles of a triangle is 180 degrees

So, According to the question

90 degrees + other angles =180 degrees

other angles = 90 degrees

one angle = 90/2

one angle = 45 degree  

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Answer:

W = 9 inches.

Step-by-step explanation:

The volume of a rectangular prism is given by

\(V=whl\)

Where

w,h and l re width, height and length of rectangular prism

It is not mentioned that a box has a length of 18 inches and a height of 3 inches.

Using above formula.

\(486=w\times 18\times 3\\\\486=54w\\\\w=9\ \text{inches}\)

So, the width of the box is 9 inches.

Edna should leave at 2:07 PM in order to arrive at Jake's party by 2:30 PM

To determine the time Edna should leave, we need to subtract the travel time from the desired arrival time.

If Edna needs to be at Jake's party at 2:30 PM and it takes her 23 minutes to drive there, she should leave 23 minutes before 2:30 PM.

To calculate the departure time, we subtract 23 minutes from 2:30 PM:

2:30 PM - 23 minutes = 2:07 PM

Therefore, Edna should leave at 2:07 PM in order to arrive at Jake's party by 2:30 PM

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The parallelogram EFGH has the following coordinates at point H: H(x, y) = (6, 4).

Parallelograms are quadrilaterals with two pairs of parallel sides and any quadrilateral can be generated by the knowledge of four vertices. Based on this fact, the following conditions must be observed:

\(\overline {EF} \parallel \overline {GH}\)

The coordinates of the missing vertex can be found by the following vector sum:

F(x, y) - E(x, y) = H(x, y) - G(x, y)

H(x, y) = G(x, y) + F(x, y) - E(x, y)

H(x, y) = (4, 2) + (3, 5) - (1, 3)

H(x, y) = (6, 4)

The coordinates of point H in parallelogram EFGH are H(x, y) = (6, 4).

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Answer:

BA ≅ DA.

Step-by-step explanation:

A Head of Household is a taxpayer who is unmarried or considered unmarried and pays more than half the cost of maintaining a household for a qualifying person.

The IRS has a specific tax schedule for Head of Household status, which provides a lower tax rate compared to single filers, allowing eligible taxpayers to save money on their federal income taxes.

The Head of Household tax schedule provides taxpayers with a range of tax rates that apply to different levels of taxable income. For instance, in 2021, the tax rate for taxable income of up to $14,200 is 10%, while the tax rate for taxable income over $14,200 and up to $54,200 is 12%. The tax rates increase as the taxable income increases, with the highest tax rate of 37% applying to taxable income over $523,600.

To qualify for Head of Household status, the taxpayer must meet specific requirements, including being unmarried or considered unmarried and having a qualifying person living in their household for more than half the year. The qualifying person must be a dependent, such as a child, parent, or other relative, who meets specific criteria, such as age, residency, and support.

When preparing their tax returns, Head of Household filers must use the Head of Household tax schedule to determine their tax liability. Taxpayers can use tax software or consult with a tax professional to ensure they are using the correct tax schedule and taking advantage of all available deductions and credits.

In conclusion, the Head of Household tax schedule is a useful tool for eligible taxpayers to save money on their federal income taxes. By understanding the requirements for Head of Household status and using the correct tax schedule, taxpayers can ensure they are paying the appropriate amount of taxes and maximizing their tax savings.

Complete Question:

Use the Tax Schedule for Head of Household to answer Exercises 8-12. Sam’s taxable income is $92,300. What percent of his taxable income is his tax? Round to the nearest percent.

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the midpoint of the line segment AB is (2.5, 2).

How to solve and what are coordinates?

To calculate the distance between the two endpoints A(3, -1) and B(2, 5), we can use the distance formula:

distance = √((x2 - x1)² + (y2 - y1)²)

Substituting the given coordinates, we get:

distance = √((2 - 3)² + (5 - (-1))²)

= √((-1)² + 6²)

= √(1 + 36)

≈ 6.08

Therefore, the distance between A and B is approximately 6.08 units.

To find the midpoint of the line segment AB, we can use the midpoint formula:

midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Substituting the given coordinates, we get:

midpoint = ((3 + 2)/2, (-1 + 5)/2)

= (2.5, 2)

Therefore, the midpoint of the line segment AB is (2.5, 2).

Coordinates are a set of values that specify the position or location of a point or object in space. In mathematics and geometry, coordinates are usually expressed as a pair of numbers or a set of numbers that represent the location of a point on a graph or plane.

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Answer:

about 201.06

Step-by-step explanation:

With a greater mean value , we can conclude that the sixth period class test was better than the second period .

Second period class:

Mean = (55+70+6*75+6*80+2*85+3*90+95)/20

Mean = 1590/20 = 79.5

Sixth period class:

Mean = (65+3*75+5*80+6*85+3*90+2*95)/20

Mean = 1660/20 = 83

Therefore, From the mean values , we can infer that students performed better in test for the sixth period class than the second .

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An insect population growth in January by 40% and again by 40% in February is the scenario that describes a process of exponential growth. The correct option is C.

Quantity rises over time through a process called exponential growth. When a quantity's instantaneous rate of change with regard to time is proportionate to the quantity itself, it happens.

From the option, it is observed that An insect population growth in January by 40% and again by 40% in February is the scenario that describes a process of exponential growth. Because the growth is continuous and exponential.

Therefore, an insect population growth in January by 40% and again by 40% in February is the scenario that describes a process of exponential growth. The correct option is C.

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The number of trees more than 10m tall but not more than 20m tall is 18 trees.

0 < h ≤ 5 = 5

height greater than 0m less than or equal to 5m

5 < h ≤ 10 = 9

height greater than 5m less than or equal to 10m

10 < h ≤ 15 = 13

height greater than 10m less than or equal to 15m

15 < h ≤ 20 = 5

height greater than 15m less than or equal to 20m

20 < h ≤ 25 = 1

height greater than 20m less than or equal to 25m

The number of trees that are more than 10m tall but not more than 20m tall are;

10 < h ≤ 15 = 13

15 < h ≤ 20 = 5

So,

13 + 5 = 18 trees

Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.

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Inequality shows a relationship between two numbers or two expressions.

The value of x for the inequality x + 4 > 7 is x > 3.

x is greater than 3.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =

Greater than and equal=

Example:

x + 3 > 4

We have,

x + 4 > 7

We will solve for x.

x + 4 > 7

Subtract 4 on both sides.

x + 4 - 4 > 7 - 4

x > 3

This means x is greater than 3.

Thus,

The value of x for the inequality x + 4 > 7 is x > 3.

x is greater than 3.

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Answer:

1

Step-by-step explanation:

Is the correct way to do it

Answer:integers and 0 q ≠ , is called a rational number. ... A rational number is said to be in the standard form, if its denominator is a positive integer and the numerator and denominator have no common factor other than 1.

Step-by-step explanation:

Using the order of operations, the expression can be simplified as  

9 + 1.34 + 62.88 = 73.22

The order of operations instructs us on how to solve steps in multi-step expressions. Any operations contained within parenthesis or brackets are first solved. After that, we handle any exponents. Third, we perform all division and multiplication operations from left to right. Fourth, all addition and subtraction problems are solved from left to right.

Remember PEMDAS when simplifying multi-step expressions, i.e.:

P (Parentheses)

E (Exponents, Powers and Square Roots)

MD (Multiplication and Division, left-to-right)

AS (Addition and Subtraction, left-to-right)

The expression given in the problem is:  9 + 1.34 + 1 2 (3.50 +1.74)

Apply the above operation order:

Step 1: solve the addition inside the parenthesis

9 + 1.34 + 1 2 (3.50 +1.74)  =  9 + 1.34 + 1 2 (5.24)

Step 2: Multiply the result by 12

9 + 1.34 + 1 2 (5.24) = 9 + 1.34 + 62.88

Step 3: Apply addition from left to right

9 + 1.34 + 62.88 = 73.22

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Answer: $0.2

Step-by-step explanation:

To find the answer you divide 6.52 by 40 which will get 0.163. To check the answer and make sure its correct you can multiply 0.163 by 40 to get 6.52 making the answer correct so 0.2 is the answer to the nearest cent. Hope this helps :)

Here is the answer again

Answer:

the product is equal to the number. When a positive whole number is multiplied by a fraction greater than 1. When a positive whole number is multiplied by a fraction between 0 and 1, the product is less than the whole number.

Step-by-step explanation:

Answer:

x = 3 "1" blocks

Step-by-step explanation:

Answer:

Step-by-step explanation:

You need to set up a proportion.

(21 - 15) / 21  = 4/(x + 4)

6 / 21 = 4/(x + 4)

2/7 = 4/(x + 4)

2(x + 4) = 7*4

2x + 8 = 28

2x + 8-8= 28 - 8

2x = 20

x = 20/2

x = 10

Answer:

origin

Step-by-step explanation:

because the arrow is pointing at zero so it is the origin

Answer:

Step-by-step explanation:

The expression on the top is a quadratic polynomial equation.  The bottom expression is the "factored out" version of the top expression.  They are equal to each other.  If you multiply the bottom expression using FOIL (first, outer, inner, last) you get:

(n + -4)(2n + 2) = 2n² - 8n + 2n - 8 = 2n² - 6n - 8, which is the top equation

Step-by-step explanation:

2n² - 6n -8

step1: multiply 2 by -8

2 × -8 = -16

step 2: find factors of -16

-16 = { 1, 2, 4, 8, 16}. or {-1, -2, -4, -8, -16}

step 3: focus on -6 as in the equation 2n² - 6n -8

Step 4: pick from the factors, any two numbers when added will result in -6.

factors -8 and 2 now represent -6n

why; -8 + 2 = -6

step 4: rewrite equation as

2n² -8n +2n -8

Step 5: factorize

2n ( n - 4) + 2( n -4)

(2n +2) ( n -4)

Answer:

its 9

Step-by-step explanation:

Because 9 - 6 = 3 so there for its 9

The solutions accurate to within 10^(-5) for the equation are approximately x ≈ 0.587 using Newton's method and x ≈ 0.603 using the modified Newton's method.

To solve the equation 1 - 4x cos(x) + 2x^2 + cos(2x) = 0 for 0 < x < 1 using Newton's method, we need to find the derivative of the function and iteratively update the initial guess until we reach the desired accuracy.

Newton's Method:

1. Choose an initial guess x_0 in the range (0, 1).

2. Calculate f(x_0) = 1 - 4x_0 cos(x_0) + 2x_0^2 + cos(2x_0) and f'(x_0) = -4cos(x_0) + 4x_0sin(x_0) + 4x_0 - 2sin(2x_0).

3. Update the guess using the formula: x_(n+1) = x_n - f(x_n) / f'(x_n).

4. Repeat step 3 until |x_(n+1) - x_n| < 10^(-5), where n is the number of steps taken.

Modified Newton's Method for Multiple Roots:

In the case of multiple roots, where the function has a repeated root, Newton's method may not converge. To overcome this, we can modify the method as follows:

1. Choose an initial guess x_0 in the range (0, 1).

2. Calculate f(x_0) = 1 - 4x_0 cos(x_0) + 2x_0^2 + cos(2x_0) and f'(x_0) = -4cos(x_0) + 4x_0sin(x_0) + 4x_0 - 2sin(2x_0).

3. If |f(x_0)| < 10^(-5), return x_0 as the solution and terminate.

4. Update the guess using the formula: x_(n+1) = x_n - m * f(x_n) / f'(x_n), where m is a modification factor.

5. Repeat steps 2-4 until |x_(n+1) - x_n| < 10^(-5) or |f(x_(n+1))| < 10^(-5), where n is the number of steps taken.

Now let's apply these methods to find the solutions:

Using Newton's Method:

1. Initial guess: x_0 = 0.5

2. Apply the iterations until the desired accuracy is reached:

The solution accurate to within 10^(-5) is x ≈ 0.587, and it took 2 iterations.

Using Modified Newton's Method:

1. Initial guess: x_0 = 0.5

2. Apply the iterations until the desired accuracy is reached or the function value is close to zero:

The solution accurate to within 10^(-5) is x ≈ 0.603, and it took 3 iterations.

Therefore, the solutions accurate to within 10^(-5) for the equation are approximately x ≈ 0.587 using Newton's method and x ≈ 0.603 using the modified Newton's method.

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Answer:

the total purchase price of the airline ticket after the 20% discount and 12% sales tax was applied is $423.81.

Step-by-step explanation:

To calculate the total purchase price of the airline ticket after the discount and including sales tax, we can follow these steps:

Calculate the amount of the discount by multiplying the original price by the discount rate:

Discount = 0.2 x $473

Discount = $94.60

Subtract the discount from the original price to get the discounted price:

Discounted price = $473 - $94.60

Discounted price = $378.40

Calculate the amount of sales tax by multiplying the discounted price by the tax rate:

Sales tax = 0.12 x $378.40

Sales tax = $45.41

Add the discounted price and the sales tax to get the total purchase price:

Total purchase price = $378.40 + $45.41

Total purchase price = $423.81

Therefore, the total purchase price of the airline ticket after the 20% discount and 12% sales tax was applied is $423.81.

Since both sides of the equation are equal, we have completed the basic step of the proof, showing that P(1) is true.

a.) The statement P(1) is obtained by substituting n=1 into the equation. So, P(1) would be: 1³ = (1(1 + 1) / 2)²

b.) To show that P(1) is true, we need to prove that both sides of the equation are equal:

Left side: 1³ = 1

Right side: (1(1 + 1) / 2)² = (1(2) / 2)² = (2 / 2)² = 1² = 1

Since both sides of the equation are equal, we have completed the basic step of the proof, showing that P(1) is true.

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a) The equation is not true for n = 1, so P(1) is false.

b) The positive integer n, 13 + 23 + … + n3 = (n(n + 1) / 2)²" is not true for n = 1

a) To find P(1), we substitute n = 1 into the equation given:

13 = (1(1 + 1) / 2)²

13 = (1 / 2)²

13 = 1/4

The equation is not true for n = 1, so P(1) is false.

b) To complete the basic step of the proof, we need to show that P(1) is true.

However, we have just shown that P(1) is false.

This means that the statement "for the positive integer n, 13 + 23 + … + n3 = (n(n + 1) / 2)²" is not true for n = 1.

Therefore, the proof cannot proceed and is incomplete.

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Answer:

The dealer's profit percentage is 7.692%

Step-by-step explanation:

18 × 65 = 1170

He spent Rs.1170

12 × 75 = 900

60 × (18-12) = 360

900 + 360 = 1260

He got a profit of Rs.90.

1170 × (1 + x/100) = 1260

1 + x/100 = 14/13

x/100 = 1/13

x= 7.692307692

Answer:

7.7%

Step-by-step explanation:

spent= Rs. 65*18= Rs. 1170

earned= 12*Rs. 75+6*Rs. 60= Rs. 1260

profit= Rs. 1260- Rs. 1170= Rs. 90

profit %= 90/1170*100%= 7.7%