prove that the sum of the squares of any two odd numbers is always even

i don’t know for sure but i just figured it out....

Answer:

C. HA

D. AAS

Step-by-step explanation:

∆HIJ is a right triangle with a given labelled acute angle and a given hypotenuse, which are congruent to the acute angle and hypotenuse length of ∆KLM, by on the Hypotenuse-Acute Angle Theorem (HA), ∆HIJ and ∆KLM are congruent.

Also, the two triangles have two given angles that are congruent, and a non-included side (hypotenuse), which are congruent in both triangles, by definition of the AAS congruency theorem, both triangles can be said to be congruent.

Therefore, the congruency theorems that could be given as reasons why both triangles are congruent to each other are the HA and AAS theorems.

Answer:

The correct answer is HA and AAS.

Step-by-step explanation:

The HA (hypotenuse angle) states "if the hypotenuse and one acute angle of a right triangle are congruent to the hypotenuse an done acute angle of another triangle, then the triangles are congruent.

The AAS (angle-angle-side) theorem states "If two angles and a non-included side of one triangle are congruent to two angles and a non-included side of a second triangle, then the triangles are congruent.

Answer:

The single transformation in this figure is reflection through the y axis at 2 y axis

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The Operating income is $172,500.

To calculate the margin of safety, contribution margin ratio, and operating income, we need to use the given information.

a. Margin of Safety:

Margin of Safety = Actual Sales - Break-even Sales

Given that the break-even point is at $750,000 in sales revenue and actual sales are $1,100,000, we can calculate the margin of safety:

Margin of Safety = $1,100,000 - $750,000 = $350,000

Therefore, the margin of safety is $350,000.

b. Margin of Safety as a Percentage of Sales:

Margin of Safety Percentage = (Margin of Safety / Actual Sales) * 100

Using the values from the previous calculations:

Margin of Safety Percentage = ($350,000 / $1,100,000) * 100 = 31.82%

Therefore, the margin of safety expressed as a percentage of sales is approximately 31.82%.

c. Contribution Margin Ratio:

Contribution Margin Ratio = (Contribution Margin / Sales) * 100

To calculate the contribution margin, we need to subtract variable costs from sales:

Contribution Margin = Sales - Variable Costs = $1,100,000 - $645,000 = $455,000

Using the values, we can calculate the contribution margin ratio:

Contribution Margin Ratio = ($455,000 / $1,100,000) * 100 = 41.36%

Therefore, the contribution margin ratio is approximately 41.36%.

d. Operating Income:

Operating Income = Sales - Variable Costs - Fixed Costs

Using the values provided:

Operating Income = $1,100,000 - $645,000 - $282,500 = $172,500

Therefore, the operating income is $172,500.

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Answer:

Area is 8000 Have a nice day!

Answer:

just multiply both

Step-by-step explanation:

understand

Answer:

Step-by-step explanation:

product means multiply

so 392 x 624 = 244,608

Answer: 92/3 OR 30 2/3 ??

Step-by-step explanation:

Answer:

it would be the top

Step-by-step explanation:

it has a negative slope and goes up 3

Answer:

see below

Step-by-step explanation:

3x+9 = 15

Subtract 9 from each side

3x+9-9=15-9

3x = 6

Divide by 3

3x/3 = 6/3

x=2

Check

3*2+9 = 15

6+9 =15

15=15

Answer:

Cost price of buying p pounds of oranges and apples.

Step-by-step explanation:

Cost price is the total amount incurred in procuring a particular commodity. It is usually calculated by taking the cost of each product and the number of products bought.

In this problem;

Cost price of Oranges = Number of pounds of oranges x cost per pound of orange

  Cost price of Oranges  = p x $2.29 = $2.29p

Cost price of Apples = Number of pounds of Apples x cost per pound of apples

   Cost price of Apples = p x $1.69 = $1.69p

The total cost of purchasing orange + apples  = 2.29p + 1.69p

So, 2.29p + 1.69p represents the total cost of purchasing apples and oranges.

The number which is represented by the expression "five more than a certain number is 4 less than one-half that number" is -2/3

let

the unknown number = x

x + 5 = 4 - 1/2x

x + 1/2x = 4 - 5

1 1/2x = -1

x = -1 ÷ 3/2

= -1 × 2/3

= -2/3

Therefore, the number which is represented by the expression "five more than a certain number is 4 less than one-half that number" is -2/3

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Answer:

Acute, Obtuse and right angled triangle are the three triangles on the basis of angles.

Equilateral, Isosceles and Scalene are three triangles on the basis of of sides.

The seven types of triangles that exist in the world: equilateral, right isosceles, obtuse isosceles, acute isosceles, right scalene, obtuse scalene, and acute scalene.

Answer:

<A= right

<B= acute

<C= obtuse

<D=  right

Step-by-step explanation:

Answer:

150÷3=50

150=1.5min

300=3min

400=4min

Question 8

It should be D) $101.35

Question 9

It should be C) It will always be less then the divisor

Question 10

It should be A) [tex]\frac{17}{18}[/tex]

Question 11

It should be C) 5 and 9

Question 12

It should be  C) y=9x-4

Question 13

It should be A) (0,1)

Question 14

It should be D) The water starts off cold and then gets hotter

Question 15

It should be D) 7.2

Answer:

[tex] 5x - 1 = -6 [/tex]

[tex] x = -1 [/tex]

Step-by-step explanation:

The model above shows a weigh balance which can be represented by an equation have two sides, of which must be equal to each other.

On the right of the equation, we have 5 "x" and 1 "-", which can be represented as: [tex] 5x - 1 [/tex].

On the other side, we have 6 "-1", which can be represented as: -6.

The equation that can be used to solve x is:

[tex] 5x - 1 = -6 [/tex]

Solve for x. Add 1 to both side

[tex] 5x - 1 + 1 = -6 + 1 [/tex]

[tex] 5x = -5 [/tex]

Divide both sides by 5

[tex] \frac{5x}{5} = \frac{-5}{5} [/tex]

[tex] x = -1 [/tex]

Answer:

Equation: 5x - 1 = -6

x = -1

Step-by-step explanation:

Hello!

The equation is 5x - 1 = -6.

Solve for x by isolating the variable.

The value of x is -1.

Answer:

It will be worth $6380 after 1 year

Step-by-step explanation:

The motorcycle cost $7250 = m

if it depreciates by 12% per year, that means it's value goes down by 12%

and that means that it now costs less than it's original cost

Hence it costs 12% less, Or, it's new value is, after taking out the 12% that it lost,

100-12 = 88

so, it's new value is 88% of it's original value,

So, after 1 year, it's value is,

New value = 88% of original value

New value = (88%)(m)

New value = (0.88)(7250)

New Value = $6380

Answer:

f(2) = -3

Step-by-step explanation:

Let x= 2

What value is y when x=2

Y = -3 when x =2

f(2) = -3

Answer:  y = 40x

Step-by-step explanation:

the answer is y = 40x  

Answer:

.6/37.

Step-by-step explanation:

Answer:

A = (2x² + 4x + 1) (8 − x)

A = -2x³ + 12x² + 31x + 8

Step-by-step explanation:

W = 2x² + 4x + 1

L = 8 − x

Area is width times length.

A = (2x² + 4x + 1) (8 − x)

If you wish, you can simplify with distribution.

A = 8 (2x² + 4x + 1) − x (2x² + 4x + 1)

A = 16x² + 32x + 8 − 2x³ − 4x² − x

A = -2x³ + 12x² + 31x + 8

Answer:

1/49 of a chance

Step-by-step explanation:

Answer:

Y=3

Step-by-step explanation:

Bc im right

Answer:

The slope-intercept form (y=mx+b) would be y = -3/4x + 25/4

Answer: y  = [tex]-\frac{3}{4}x + \frac{25}{4}[/tex]  

Step-by-step explanation:

Formula: y = mx + b

Answer:

i can try :)

Step-by-step explanation:

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

First we will go find the angle measure of 3.

We already know that <1 & <2 are 55° & 60°.

Tip: The sum of all the angles in a triangle is 180°.

So now if we add those two angles we'd get 115°, then we could subtract it from 180 to get the measure of <3, which is 65°.

For <4 it should be easier if you know that line AB is parallel to line CD and then line AC is the transversal because it goes through both lines.

Tip: Alternate interiors are angles that are equal to each other.

Then when you know all this you can figure out that <2 and <4 are alternate interiors which makes them equal to each other. So if they said that <2 is 60° then it'll only make sense if <4 is also 60°.

Now for <5 we know that <3,<4, and <5 are all on a line so that makes the sum of those three angles 180°.

So we would do the sum of <3, <4, then x and all that is equal to 180°.

[tex]65+60+x=180\\125+x=180\\x=55[/tex]

Great now we know <5 is 55°.

We will now move on to <6. It has the same relationship to <4 as <2 and <4. So if <4 is 60° that means <6 has to be 60°° as well.

Tip: The sum of these two angles (in this case are <5 and <6) are equal to t the outer angle (<7)

Now we have to figure out the measure of <7. First we have to notice that if we add <5 and <6 we will get <7. So 55 + 60 = 115 and that's it <7 is 115°.

Now the recap:

<3=65°

<4=60°

<5=55°

<6=60°

<7=115°

Answer:

h(-2) = -5

Step-by-step explanation:

Step 1: Define

h(x) = 3x + 1

h(-2) is x= -2

Step 2: Substitute and Evaluate

h(-2) = 3(-2) + 1

h(-2) = -6 + 1

h(-2) = -5

Answer:

0.14285....

Step-by-step explanation:

Long division